It sounds like a similar problem that all chevy owners sometime at one point had. Your starter solenoid gets too hot and won't allow the starter pinion to engage.
Them after a period of time, when things cool off, it starts.
If this is the problem, they make a lot of different ways to solve the problem. The one I use on my big block is a remote ford starter solenoid. They sell this kit at Jegs or Summit or you can do like I did and make your own. Painless Wiring also makes a kit called Hot Shot. They make heat sheilds that bolt over the starter solenoid. There's a lot of options.
69 Camaro, 496, 10.34 @ 134.77 mph.