As part of the design on Ventures...the fuel pump will only cycle for a few seconds with
the engine not rotating (or detected**). This allows for refilling of the carbs before cranking but prevents a major fuel loss from a leak.
If you had the pump discharge routed to a catch can, the pump will only run a few seconds with key on and then stop, if no engine rotation is detected. If you cycle the kill switch off and back on, it should repeat this short pumping time.
If the discharge hose is connected to the carbs, as they fill up and needle valves close off the pump will slow down and stop. If the carbs are full the pump will not cycle.
The pickup coil detects crank position and sends a signal to the Igniter so the ignition can be timed to occur at the proper crank position. If the pickup coil is not working, rotation is not sensed and ignition will not occur, and the fuel pump will not operate either.
I would test the pickup coil first.