this has to be an easy fix. my 63 will start, run for about a minute, then stop. it may start again, then it may not. if I wait about 15-20 minutes, it will start, run about a minute, then die. this truck is a work in progress so I have not been running it regularly. I changed out the fuel filter (stone type, at the carb) thinking it was varnished up. no luck.
Rust, corrosion, and general crud could be blocking the pickup tube in the tank. But you should eliminate the more obvious causes first. Rebuild the carb, check the fuel pump output pressure, electrical gremlins like plug wires, distributor cap, rotor, points etc. Val