K...solid advice from the gang here. I am also familiar with the GM wiring of the era and the worst thing in the Pontiac was routing the starter wires through a metal tube inside the exhaust manifold!...a recipe for heat all the time. Not only that but the wiring really was insufficient for the amps drawn by the solenoid on top of the starter...about 50 amps.
Like the guys said, hot soak, purple starter wire etc, melts the insulation in that tube and it shorts out, with the car off just wiggle that starter cable that goes in the tube, it might move it off the short, try it a couple of times and then see if it works.
Real fix is what I just did with the stuff from MAD electronics, mounted a Ford Magnetic switch on the fender. Some call it a starter solenoid, but technically it is not. The you jumper the starter permanently, mad supplies the bus bar.
Then you reroute the battery cable wire as the only wire to the starter down the front past fuel pump along the oil pan. You put a bus bar on fire wall and near front headlights, with headlight relays as well.
Now when you turn the key you won't believe the difference, fires as a brand new car, full amps to starter, no heat soak worries. I put halogen headlights in and a 12 si alternator 78 amps instead of 63. The dash lights are brighter, because the headlights don't draw the power through the dash harness, and the cable to the starter is only live when cranking....no other time. Nothing goes though the metal tube.
The inside dome light will burn your retinas out, all systems full power. At 550 RPMs at idle in drive with high beams on, radio, blower still charges at 14.6 amps.
By the way I had put in a brand new wiring harness two years ago from American auto wire. Top quality....but that heat tube had melted the insulation on the starter S wire...it will eventually.
Talk to Mark at MAD electronics, he ran an auto electric shop for years....if you drive it and want super starts, power, strong lights etc...even easier to change the starter, one big cable.....that can carry all those amps!