Having issues with my 71 GTX, 440-6 4 speed. Car was running fine on a recent drive. On the way home it started missing and proceeded to get much worse. It got so bad I decided to just park it and get it towed home. I figured it ate the points so I put a new set in and it wouldn't start. After messing around with it I discovered no spark coming from the coil. I then installed a new coil but lo and behold, still no spark. I started going through a diagnostic evaluation (instead of just throwing parts at it) and I really couldn't narrow it down. Points are good, condenser checked out, rotor checked out. Voltage at the coil was 11.8 with key in run position, 9.6 or so in the start position. Without really fixing anything car then started and ran fine. I then decided to drive it around and it ran fine for about 5 minutes and then started missing severely. Car died a couple of times trying to get it home and then when I limped it onto my street, it smoothed out and started running o.k. again. I got home and did the only thing I could think of. I got a cold beer and just looked at the car for awhile. I started thinking that something must be getting hot?? and shorting out in the ignition system. I have many new ballast resistors in stock so I placed a new ballast on the car. I checked ohms resistance on the new ballast before installing and it was .6-.7 ohms. It started right up and was running fine in the garage. I was under the hood just looking and noticed that after running for a minute or so the new ballast started smoking. I shut the car off and there it sits. I then finished my beer.
I'm thinking the problem is in the ignition run circuit (the Blue wire that comes out of the ignition switch and ultimately is on the run side of the ballast and is also one of the field wires off the back of the alternator).

The blue wire feeds the resistor for the ignition . So any excessive draw would be from the ignition side. The regulator and alternator are fed on the same input side or supply side to the resistor. The charging system is not on the resistor side. The resistor will get hot and a new one may smoke until the coating wears off. Try a new condenser. I have seen many failures. Also make sure the distributor lead is not grounding out in the distributor attachment area or condenser lead. Also make sure the coil is for an external resistor.

condensor

Sounds like an intermittent continuity issue on the primary side.
Making-Breaking Contact. Worst after some time (i.e. heating).
Condition on those wirings & connections?
Old/New wiring harness?

Higher rpm == higher amp load on ignition circuit.
May run OK at idle, then crappy otherwise.

If/When you have it idling OK, wiggle wiring & observe.

You need to check it with your volt ohm meter when it gets hot and acts so you can trouble shoot it properly
It might be the wires under the dash to the bulkhead connector or from the bulk head connector up to the resistor or some where else
Look for the voltage drop first and then for higher resistance
It is repeating now so go find it

Check the connector at the base of the steering column. Mine was loose fitting and caused the engine to misfire and die. Luckily my foot brushed against that connector when I got out of the car and the engine misfired. If that wouldn't have happened, who knows how long I would have been chasing that issue. It could also be any connection on that run wire. Check them all.

i second the steering column connector.
i have repaired a fair amount of those that have gotten "melty" over the years. sometimes they are hard to see.

Quote

I was under the hood just looking and noticed that after running for a minute or so the new ballast started smoking

The above is not totally uncommon as they do get pretty hot. Any residue on them will cause them to smoke for a short time. Otherwise I would say a flaky condenser or connection. Check the ends of the coil wire, I was chasing an intermittent ignition problem one time and found a bad connection on one end of the coil wire. It had been arcing for awhile and burnt the cap and center conductor quite aways up inside the wire.

post what it ends up being

Maybe the coil is simply drawing too much current??? I agree that really hot ballasts are not uncommon.