i noticed in your picture showing a splice to the voltage regulator from the ballast, you used a "scotch lock" [or whatever they are called]
i'm not a fan of those, as they can cut the wire strands when they are attached, and can allow moisture to wick into the spliced wires causing the dreaded "green death".
just my opinion from years of repairing wiring harness issues.
your mileage will vary.

I had the same problem your experiencing a few years back with my 70 Satellite...

It didn't always want to start as it should and seemed like there was no power in the start location of the switch...

Occasionally you could turn it over and flip the switch back to run fast and it would fire...

It turns over just fine but never tries to start...

Mine ended up being a bad ignition switch not always supplying juice to the run 2 terminal...

Sometimes it was fine...other times it didn't start...

You can always turn the key to the run position and jump the starter relay and it will start...provided everything else is in working order...

All ignitions in my cars I've done in the past ten years I scrap everything original and run all aftermarket components...

My last 3 builds are all full MSD...

No more issues...

OMG!!!! 😳 Electronics 101A teaches that every connection is a potential problem and to avoid them whenever possible. You have some rewiring to do IMO.
And the U-haul connectors (scotch loks) as mentioned GOTTA GO. They're right up there with the bolt on .99 cent battery cable ends

EDIT :
Mr. Kunkle was referring to the coil sparking when the male terminal was momentarily grounded.

With regards to the ECU, I would get the charging problem resolved as 16V will potentially fry them

Not sure what you have going on with that wiring. The voltage regulator looks older, you may want to replace it with a modern solid state one. That being said, newer parts these day are not always better than older ones that are still working well. Do not buy the reproduction early style voltage regulators, they are junk.

My brother had a similar problem to yours years ago and it wound up being the ignition switch. Running a 12 volt source to the coil should have eliminated that as a potential problem though.

Modern ECU replacements leave a lot to be desired. Jegs sells a decent replacement. Their orange box is good to about 5,500 rpm and their blue box is essentially the old chrome box. Bill Evans can also sell you a reproduction engine harness that is made for electronic ignition.

MSD blaster II coils are not recommended for use with stock style ECUs. They are also not meant to be mounted horizontally. I would replace the coil if you buy a new ECU. Bad grounds are also a common issue with ECUs. I have a ground strap from the back of my block to the ECU as an added fail safe.

When you check for voltage, always jiggle the wires a bit and see if the meter changes. We’re talking about nearly sixty year old wiring here, might detect a broken wire or bad crimp connection.

As I stated in my initial I know very little about wiring. I admit that the wiring is old and was done before I ever bought the car so I don't know what they did.

Ballast Resistor - The diagrams I have only show 4 wires on the resistor. But as you can tell from the picture I have a couple of double wires for a total of 6 wires. Does any one have any idea what the 2 extra wires are for? 2 blue wires go into the wiring harness. I think one goes to the coil but I am not sure which one - Left side or right side? and I don't know where the other goes.

I can read wiring diagrams but since this is a 67 and has a later electronic ignition system on it that part will be different. Does anyone know where I can get a modified wiring diagram that shows how the electronic ignition system ties into the 67 wiring?

The coil is mounted to the top of the compressor and is in an almost vertical position. I did buy another ECU and put it on but the car still did not start. So it has to be in the wiring. For me it is going to be a task to replace it as I don't have that much time anymore and don't get around as easily as I used to.

How do I get a hold of Bill Evans to get a 67 engine wiring harness modified for an electronic ignition?

You folks have been a great help and I appreciate it. I will let you know what happens. Take Care.

If you go back to John Kunkles post
And my later Comment
EDIT :
Mr. Kunkle was referring to the coil sparking when the male terminal was momentarily grounded. IE: Ground the mail terminal on the ECU side of the distributor distributor connector, and the coil wire should emit 1 spark every time you ground it

With regards to the ECU, I would get the charging problem resolved as 16V will potentially fry them.
I also agree with the VR upgrade. There will be no resistors on the back of an electronic regulator.

Slow progress. I have ordered a VR (Echlin from NAPA) and should be here tomorrow. Still working on the splice issue.

I checked the 4 pin ballast. I found that the 5 ohm resistance pins are on the bottom and the 1.5 resistance pins are on the top. Does that make any difference with the wiring and in the start / run operation?

Thanks.

Additional note. I have a 4 pin ECU and a 4 pin ballast resistor. I can find wiring diagrams for a 4 pin ECU and a 2 pin ballast or for a 5 pin ECU and a 4 pin ballast. But nothing for what I have. Does anyone know where I can find a wiring diagram for my setup?

BTW I no longer get a bump when I release the starter.