JMcrae,
The lift is only supposed to turn on for 2 seconds when you first turn the ignition key to the run position. If you bump the starter (without starting the engine) and leave the ignition in the run position, the lift should immediately turn on and run for approximately 25 seconds.
If the above isn't happening, then the first thing to do is measure the voltage present at the lift pump wiring harness to try and determine whether you have a problem with the lift pump itself or its supply voltage. The Yellow/White wire should have approximately 12 volts when you bump the starter. The Black/White wire is the ground.
If you don't have 12 volts present on the lift pump wiring harness when you bump the starter, then you either have a problem with the wiring harness between the ECM and the first pump, the ECM connector, the ECM itself, or the ECM grounding. There's no fuse or relay between the lift pump and the ECM.
If you are measuring 12 volts on the lift pump wiring harness when you bump the starter, then the lift pump is the problem. If you decide to replace it, go with an Airtex replacement. It's only $150, a better design from the original Carter, fits in the same location as the original, and works *great*!
Good luck,
John L.