The next time it fails to start when hot, climb up to where you can see down the throat of the carburetor to see if you get a squirt of fuel when you goose the throttle. If not, you may have a marginally functional fuel pump. (Push starting makes even a marginally functioning fuel pump work much faster than the starter does, which might explain why a push start makes it fire right up.
If you pass the fuel test, attach a hot wire between the ignition key side of the ballast resister and the coil. A wire with alligator clips on each end works nicely for this. (You should keep one of these in your glove box anyway for when the ballast resister burns out. It will allow you to limp home.)
If it won't start then, attach the jumper wire from the big wire on the starter to the coil. If that doesn't work, you may a have a coil on the way out. They are prone to failing while hot. After the engine is shut off, and air no longer passes over the faulty coil and will soak heat from under the hood, making it fail until it can cool off.
It is possible to have an ignition coil and a fuel delivery issue at the same time.
BTW, these tests do not require any new parts.
Carl
