83 Toyota Tercel. New starter.
On occasion will not start... battery good, all lights come on, just no start; as though power not getting to the starter. I let it sit for two or three hours and it starts like nothing is wrong.
Sitting for a few hours... could it be it has to cool down? Dry off? Very puzzling.

Mechanic checked connections... could not tell me why this is happening.

VW Jetta's had this issue with too much heat on the starter. Once it cooled down it worked. Solution was to run a flex air hose onto the starter. With a 30 year old car could be a lot of issues.