Old truck not starting intermittently

My wife and I bought a '51 Chevy pick-up, with a 409 V-8 engine and some modifications, so different parts are different ages. We would have appreciated an all original truck, but found we liked the appeal of '05 Cadillac leather seats, stereo, AC and a tilt steering wheel, etc. There is one quirk we don’t like, however: Sometimes when we stop and park the truck it will refuse to start again. There is sometimes a loose wire on the fuse block, but that doesn’t fix the problem. I can get it started, normally after a while off and parked, but I have to put it in drive and push it a few feet. Sometimes it takes a few tries, but that generally starts it. Formerly it had a racing cam and a hole in the exhaust system. In the condition it frequently stalled and didn’t run smoothly at low rpm’s, but went like a bat outta h&#l at higher rpm’s. And the sound was distinctive from three blocks away. What might be causing the failure to start, now? It’s only happened three times in the past year, but can be aggravating and time consuming.

Dead spot on the starter…replace the starter.
While pushing it that few feet with the tranny in gear allows the starter motor to turn enough to get to a good spot. Then it will start.

Yosemite

My guess is a broken tooth or two in the flywheel, which engages the starter.

When you try to start it, the starter whirs but the engine does not turn?

Or the starter does not turn at all? In that case Yosemite has the correct answer.

I would like to know how moving a vehicle will turn the starter, as far as my experience goes when the starter is disengaged it stays disengaged.

But it will turn the flywheel, so the starter can then engage.

If it is a broken or bad tooth situation @BillRussell or maybe the starter does not mesh if a tooth is in just the right spot.

correct.