Here it is in a nut shell-For full disclosure, I have limited auto mechanical skills.
71 challenger 318 built into 340 clone fully restored in 2012 and when I picked the car up it was 100%, every light, buzzer, gauge worked as it should. Standard dash was converted to rally. Mopar electronic ignition conversion. Mopar original repop yellow cap battery. Car ran flawlessly for 4 seasons with the exception of some thermoquad tuning issues. In 2014, I installed a repop "rim blow" steering wheel. The repop wheel has a non functioning horn switch but it did have a tab for the horn wire to attach to so I hooked it up to it so it would not be floating around in the steering column. The car was driven for weekend shows and cruise nights with no issues. Right before the end of show season, Oct 16, I had the car outside my garage running and out of the blue the horn began to beep. I thought that was weird and I disconnected the horns by removing the wires at the horns. At that point, I didn't even remember that my rim blow had a non functioning horn switch and I drove it a couple more times with the horn DC'ed and put her away for the winter. Fast forward to Feb 17 and I send the car to my regular mechanic (friend since high school, totally trust him, 50 years old, several muscle cars in the 80s) to get new leaf springs installed and while he has it see if they could swap a different thermo quad on there and try to tune it right. I get the car back and when I drive it home from the shop, I notice the oil pressure gauge is not working. I get home, check under the hood and find the oil gauge wire disconnected from the sending unit. I figured it got knocked off when they swapped the carb and I reattached it and put the car back away for the remainder of the winter. April 17, The weather breaks and I take the car out for it's first run. I now notice that my oil gauge has activity but all 4 gauges in that pod are now acting funny. Gas gauge bouncing way more then normal, sometimes looking like no power and just falling limp, Temp gauge working intermittently, charge gauge all over the place and oil pressure also working intermittently. Mind you sometimes all or some go back to normal operation. Talk to mechanic, says nothing to do with changing springs or carb. I drive the car for about and hour and put it back in the garage with trickle charger on as usual. 5 days later I try to start the car and it won't turn over, clicks like dead battery. Volt meter shows 13V at battery. I use jump pack to get it started, back it out of the garage and figure I will let it run to charge up the battery. The car runs for about 3 minutes (gauges working at this point), I hear a pop, immediately smell electrical burning and see light smoke outside the windshield coming from the voltage regulator. I shut it down and remove voltage regulator, the back of it has a melted spot and smells burnt. Talk to mechanic, it's Sunday and he is out of town but instructs me to replace new voltage regulator and then check charge gauge operation. I replace voltage regulator but before I jump it again I tried to hook up the horns to see if the battery has enough juice to beep them. Headlights working the whole time. When I connect the wires, It sounds like the horn it trying to beep but really not working. I remove the center cap or the steering wheel, DC the horn wire from the fake switch, now I try to operate the horn by grounding the wire to the steering column and as soon as the wire touches metal, the key in ignition/door open buzzer begins to operate, no horn. Weird. So I now use jump pack again to start car. Car starts right up, but now the only gauge that is working is the charge gauge and not only are the other three gauges in that pod not working but everything inside my car is not not working, no tach, no clock, no dome light, no key in ignition buzzer, no lights at shifter in console. Can't get back in touch with mechanic so I let it run to try again to charge the battery. It runs for about 10-15 minutes and I want to test the blinkers, as soon as I put the blinker on the car stalls. At this point I want to give up and just get the car back in my garage until my mechanic can get to it. I jump it again, try to put it in gear and it stalls so that is a no go. Get back in touch with my mechanic. He instructs me to look for burnt wiring/fusible link. I start at battery, inspecting wires, work my way to ballast resistor and when attempting to remove the top wire it crumbles in my hand. I replace that, car starts only with a jump, I pull it back in the garage and now it is time to get her fixed so I can get a few hours on her before I trailer her to Carlisle. I know this is a lot to digest but if any of you have some guesses of what may be going on so I can give my mechanic any ideas I would be forever grateful.

Is there a fusible link that protects the interior gauges and lights? Possibly the pop I heard?

Dude! Hopefully you have a factory service manual for the car??? Usually the fusible link will knock everything out especially the alt. gauge. Crumbling wires are not good and will start fires pretty easily so check it out proper. I would imagine your problem lies in the charging/starting system so start there. Alt. may have gone full field resulting in the regulator pop.

All the wiring that I have checked under the hood and around the interior fuse box is in good condition. It was the ceramic ballast resistor that crumbled.

Actually I'd say you have good auto mechanic skills, just a bit green (lack of knowledge).

Look at the power flow diagrams on this page
http://www.heritech.org/cuda/Charge.html
This will help you understand most of the things you observed.

At the bottom is a simplified '67 wire diagram of the charge and ignition.
Your '71 will be similar except for a couple of things.
Of the top of my head, the alternator field circuit on your '71 will not ground internally. Instead it will have a ground wire coming back to the voltage regulator.
Also not shown in my '67 wire diagram is that engine instrument gages have a voltage regulator so the sending units all get 5 Volts.

Whatever the problem turns out to be, you're taking a big chance with repo battery the way you are jumping it off from what I'm told. Those things are really charge sensitive, and you can fry them from over charging it. Read the instructions on how to charge a dead one.

1. Check that your engine and body grounds are good
2. Check the useable link
3. Check that the positive on the alternator is good
4. Check the main bulkhead connection

Assuming you have a new or properly repaired wiring harness because you said it was fully restored. You may be in an OK position.

If the harness is old and it's just a cosmetic restoration it could be a crap shoot.

I can sit here and tell you from your description It seems like several things are happening at once namely a bad horn switch. Also an old battery & voltage regulator caused the death of the fusible link/other wire. Those things can easily cause all your symptoms BUT it's best to start looking at the whole of it because electricity has a mind of it's own.
The fusible link is the connection of your cars electrical system to the battery. If it's bad it can cause all kinds of power fluctuations that can affect gauges, lighting malfunctions, random stalling when electrical devices are turned on etc.

Start with #1 That battery is 5 years old. I suggest for the diagnostic portion at least replace it with a new or known good battery.
#2 Inspect the fusible link. Sometimes when the fusible link starts to go it can cause intermittent connection between the battery and the alternator/under dash wiring. The Ammeter displays how much current is going into the battery and not the amount the alternator is putting out. If the fusible link/connection is bad, the alternator output will appear normal because it isn't discharging or charging the battery. DO NOT CONFUSE A FUSIBLE LINK WITH A REGULAR WIRE. It is designed to be a type of overload protection, quite literally a fuse. If you are not worried about OEM appearance you can get a roll from Napa for about $10 that would probably last you a long long time. If you want OEM, while you order one, use the generic NAPA one to replace the burnt one for the short term. A fusible link will often look OK when it burns but will be crispy feeling and often stretchy. It is the wire from the bulkhead connector going to the battery. It will usually have a rubber tag on it that says Fusible link on it.

#3 Get your alternator tested just to be sure it's OK.

Now for some of the checks you need to look into.

Inspect the wiring for melted wires. Pay particular attention to the large wires going to the alternator, under the dash behind the fusebox and connected to the ammeter. Check the bulkhead connections and the ignition switch connections for burnt degraded connections. Again paying special attention to the large wires.

My biggest cause for concern is the burn wire to the ballast resister you described. There are 3 wires to the ballast resister. One from the crank/start circuit, one to the coil and the other is the run circuit wire. For those wires to get burnt it could be a sign of a bigger problem or it could be a coil shorting out so check the coil to be sure it's in resistance specs.

If inspections leave you warm and fuzzy about the condition of the wiring harness then check for good connections before you install the new battery. Use a battery powered circuit tester or an ohm meter to check the connection from the main alternator wire (disconnected from the alternator while testing) and the battery terminal (No battery connected while testing).
Check the blue and green wires from the voltage regulator to the alternator (both disconnected). The green wire should get connection at both ends and not be shorted to ground. The blue wire should get connection at both ends and connection to the battery when the ignition is in the run position.

Wiggle the wires while checking to be sure they are not getting intermittent connections.

Next check the horn switch for connection to ground. An ohm meter may be better than a test light here because it can check for even small amount of connection. If you suspect the switch then disconnect it for now.
After you get the battery back in and connected. Connect the horns. If they honk without a button pull the horn relay on the fuse box and check it for problems. If they honk and the relay is pulled the problem is in the wiring.

The wires to the horn run along side the main alternator wire inside the engine harness IIRC. If the harness is starting to melt/degrade the horns may be getting the power from there but they would never turn off or would honk constantly while running. If so you need to start unwrapping the wiring under the hood and inspect it.

Let us know what you find.

Here are the basic wiring diagrams for your car They are important when you look for problems.

One more thing,, if the wiring harness is new, what brand is it?

Wow IMGTX, I can not thank you enough for that detailed run down and the electrical blueprints. This info will be very helpful.

To be clear the wiring to the ballast resister appears to be in good condition, it was the ceramic portion of the ballast resister that was brittle and broke apart with little effort.

71birdJ68, When the car was restored the original harness was completely broken down, inspected and modified to run the new rally dash. I was just reminded that I did buy a rally dash wiring conversion kit but can't remember the brand.
I am working a 24 hours shift today but hope to have some time later this week or over the weekend to check some of the things IMGTX spelled out.

Thank you to everyone for the help so far!

That is usually a good thing. Those resistors are tough and rarely crumble but that is much better than a burnt wire.

Good possibility it got hit and cracked while somebody was working on something under the hood. Still check the coil resistance to be sure it isn't drawing too much current. Very doubtful it would cause a problem with the resistor even if it was shorting but better safe than sorry.

The shop found a crack in the battery. New battery, voltage reg and ballast resistor and car starts and runs. Alternator is charging at 14.5. Dash cluster being sent back to Instrument Specialties for testing. Clock, tach, gas and oil not working with power present at the back of cluster. Overhead dome light blub was shattered.??. He didn't look at horn yet. No wires or connections found burnt or even in questionable condition yet.

Crack in the battery was probably from freezing while discharged.
The common part of the gas, oil and temperature gauges is the 5V regulator. The factory one was mechanical, the rebuilt dash may have had an electronic one.
Sounds like you are on the right track.
Craig
PS My newest truck is a Ram 4500 Type 6. We have two of those now and a Pierce Type 3. We are pretty much a Pierce shop for the fleet.