When it come to electronics, pretty much any electronics, I'm lost and first to admit it, BUT this is similar to something I had on a previous Mustang I owned.
I know you've been going through a lot with trying to get this old girl going, but I really think you need to go to the ground cable. It connects from the battery to a CLEANED location near the voltage regulator on the apron and then to the FRONT of your BLOCK, not heads. There is a 3/8th bolt hole near the bottom for this. There can be NO paint or oil. Needs to be squeaky clean and good tight bolts. From the little I know, I think the circuit is trying to go to ground through whatever it can find.
If you can't locate that point, I can picture the ground cable on my car and post it. Buy a new and correct ground cable if needs be from NPD, Summit or CJPP, but it needs at least the two points of contact. Some have said to install an extra ground strap at the back of the block as well and it can't hurt.