I never looked into it to deep, but they had to make it so the lift pump would not run when the engine was not running. This is a safety feature to prevent the lift pump from pumping all the fuel out if your in an accident.
In order to allow the truck to start they had to allow the pump to run enough to push fuel to the Injection pump, but still shutoff after X seconds if truck does not start.
Not sure if they use the Oil pressure signal to tell the ECM "yes the engine is running, turn on the lift pump" or not.
I had a problem where mine would not start after replacing a lift pump. I had a gauge with 3' of hose on it so I could see it from the windshild. I could see the lift pump running for 25 sec but it would not purge the air out of the system.
I messed with it for hours, got mad and took off the gauge before I had it towed to the dealer. before calling I tried once more without the gauge and it started right up
Seems the 3' of hose on the gauge was full of air, and even after 25 seconds the liftpump would be trying to compress this air in the hose and could not purge the system.
Anyway, do you see a voltage for those 25 seconds after bumping the key? I bet you could jumper 12V to the liftpump (after disconnecting the ECM wire to the liftpump!) and see if it runs that way.