[Fullback66]

Originally Posted by Greg Reid

I learned something a couple of years ago for the first time after years of chasing that problem on various Pontiacs. Make sure that the ignition switch wire going to the 'S' terminal on the starter is getting at least 9 or 10 volts at the solenoid. I know it's not easy to do in a parking lot but if you can pre-rig a jumper from the 'S' terminal to someplace you can get to it you may find that only 4 or 5 volts is present there when it refuses to start.
That purple wire can get baked and develop high resistance after a few decades. I spliced a new wire from the firewall to the starter and it never happened again. I didn't have to pull the ignition switch but you could do that and replace the entire length.

Thanks!