The "run" wire to the coil should be thru the coil resistor. On the later (55.2) stomp starter switches there's a small terminal for the jumper wire to the coil (bypasses the resistor.) See Pic. That second wire is hot only when the stomp starter switch is depressed. With that setup, the engine should start and run as long as the starter switch is depressed, but would die as soon as you let the starter pedal return unless the ignition switch is in the run position, or if the "run" terminal doesn't have power, which might be what's happening in your case. You can troubleshoot your switch with a multimeter or powered test light. If you don't get continuity between the battery and run terminals with the key in the on position, then the switch is the problem.
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Last edited by klhansen; 10/24/2024 10:12 PM. Reason: added pic

Kevin
1951 Chevy 3100 work truck
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1929 Ford pickup restored from the ground up. | 1929 Ford Special Coupe (First car)
Busting rust since the mid-60's
If you're smart enough to take it apart, you darn well better be smart enough to put it back together.