Not saying this is your problem, however I had a situation like this with a van I owned back in the late 70's. Sometimes after driving a distance and shutting down for gas or a quick snack, the van would not start. I don't recall if it even "clicked." I tried by-passing the solenoid thinking that was the problem. Still no starter action.
I finally noticed the problem occurred more often in hot weather. Figured it out... the starter was overheating from being too close to the exhaust manifold. If I let it cool down a bit, it would eventually crank and fire. If I was in a hurry, a little ice on the started case did the trick. I installed a heat shield (I think it was a recall thing) between the starter and the exhaust/block and never had the problem again. I don't think the problem had anything to do with the starter per se, as the van was fairly ('78) new at the time.
I hope this helps you or some one else down the line.
Robert
Huntington Beach, California