^^^ Exactly. There's a terminal on the starter relay (remote mounted Ford solenoid) that powers up when the starter's cranking. That power goes to the fuel pump on the selected tank. When the engine starts, the oil pressure switch closes and the pump relay is energized through the ignition switch in RUN position. I've jumped the wire from the solenoid to the battery to run the pump and fill the carburetor. I've also run the vehicle by powering that same wire from the ignition key in Start or Run. Not recommended.
Anyhow, OP told me the engine would quit AS SOON as the key was released from Start into Run. Not that it ran in Run till the carburetor ran dry. So the ignition was quitting... He got it to keep running by hot wiring one of the terminals on the Tank Select Valve, so I'm confused about the cause and the cure on that one.