Hmmm. I remember my Vette doing something like that. Turned out to be the solenoid on the starter. We do have a solenoid on the PT. Could be dead spots. You can see the starter and solenoid if you look down in front of the engine when standing at the front grill.
In the old days we used to bang/tap on the solenoid when it was going bad to get it to start. Don't know if that would work now.
