Ram 1500 no start

My Ram 1500/auto will fail to turn over or make any clicks or noises. Lights
and dash come on with turn of (not a smart)key, but starter does not engage.
Walk away for 20-30 minutes, come back and it will fire right up every time
This usually only happens after a short trip, with a restart attempt after just a
few minutes, like a trip to the post office. Come out and nothing. I tried
starting in neutral, replaced the ignition module. The battery/starter are fine.
So it seems to me that there is a sensor that sometimes heats up at startup,
and needs time to cool/reset?  Maybe an auto shutoff relay is going bad?
Neutral Safety switch, though I would think it would start in neutral if that was
the case. I am at a loss, and just don't trust driving this anywhere without
leaving it running. Any ideas?