When the engine is hot the starter it will not work. When I run a wire from the battery to the neutral safety switch it starts. Also, after it cools down it starts.
Most common problem those years, usually it is a wiring issue, wiring to solenoid start terminals gets burnt near the starter where it is close to the exhaust manifold. also the ignition switch gets burned out, check the switch and connectors for indications of over heating (burned). If there is no soleniod heat shield on the starter this can be the root cause, install a heat shield linked below, but check the wiring also.
Check the wiring for fatigue and burns near the manifold, repair as necessary.
Also you have to check the entire starter solenoid circuit path from the fuse box to the starter for problems. Fuse box >ign switch> neutral safety> starter solenoid, look for overheating of the terminals and wiring.
Also install a "new" starter with solenoid heat shield.
Stock starter heat shield below.
I agree with much of what Moab wrote. Often times when a car gets to the age this one is, all of the connections get worn or dirty and have more resistance than they should. Add heat to a starter, and low voltage won't make the starter solenoid engage. After installing the shields stated above, if it still gives you trouble starting hot, you could wire in a relay that will allow for more voltage to get to the solenoid "exciter" terminal. This will by pass the connections so that the power comes from the battery, through the relay, to the starter. Less connections, more voltage. A three or four pin relay, some spade terminals and a couple of ring terminals, and some 10 gauge wire is all it takes. Three pin: grounded through the body of the relay, so it must be bolted to the body of the car, the small exciter wire from the starter goes to the coil/engage pin, battery power from the battery terminal goes to one of the other terminals, and run the other terminal from the relay to the starter terminal. Four pin: same as above only you have to make a ground wire to the 4th terminal, going to a ground on the body or engine.