I have a strange intermittent no start condition. Typically when the car is cold it will start fine. After few short trips, it will not start. Meaning, I turn the key, and there's no sound...no clicking, buzzing, cranking, nothing. If I come back later when the car cools off, it will start and be fine for a day or two.
Sometimes if I move the shifter from Park to Low and back, it will help it start, although, I can not be certain. Maybe it's just a coincidence.

The starter will only engage if the car thinks it is in P or N. Lets suppose that the PNP switch is starting to go south and one of the contacts is worn a bit. You shift to P, but the PNP doesn't register that. When the metal bits cool, they contract and make contact again. Rowing the shifter will also work for a while.

You could shift to N to try and start the car.

Klaus
--
Did you do your Random Act of Kindness today?

No crank or sign of life from the starter solenoid? Do the headlights and windows
work when you have the no start condition?

Can be crappy battery cable connections.
It can also be corroded out crimp-on terminals where the heavy wire
corrodes inside the crimp.

Clean up all the battery cable connections and look carefully at the cable crimps.

Bill

Starter motor.