It sounds like you have a short to voltage somewhere. When i turn the truck off the fuel pump continues to run.

Fuel Pump Won T Stop Running Third Generation F Body
Fuel pump stays running. When you turn the ignition on even without starting the engine that activates the fuel pump and also pressurized the tank. Fuel pump fuse ecm 11 20 amp is blownis the fuel pump linked t. Combined with the other issues you stated its most likely the pcm. Suspect the fuel pump relay. I suggest you check the net for info on how a fuel pump relay works and conduct the electrical test. Hello i have a 2008 sierra sle with a 53 engine.
Remove the connector the retainer screws then pull it out and open it. If it is stuck the pump could continue to run. Sounds like the fuel pump relay in under hood fuse box try finding another next to it thats the same from the headlamp relay and swap them and see if it helps. A fuel pump should pump all the time when the engine is running there maybe if its fuel injected a pressure regulator to ensure sufficient pressure is there otherwise it is. Look for signs of moisture burn marks or leaking capacitors. No its not the fuel pump thats running but the purging system.
Normally the fuel pump relay operates during starting and when turning off the engine. Anytime the fuel pump stays running with the key on its either a stuck fuel pump relay or most likely a bad engine computer pcm. The only way i can get it. I swapped the ac compressor relay with the fuel pump relay in the fuse block but that did nothing. A full explanation of how the relay works and how to check it is quite long. If the pump runs with the relay removed its not the relay.
Help i need help understanding how fuel pump relay stays energized on 2002 chevy expressi have lost secondary spark no spark at plugs. I tried pulling the fuel pump fuse and it still kept running. Now the transmission does not shift properly and the fuel pump seems to keep running. Therefore the purging process stops to allow the gas tank to be pressurized only a few psi of pressure and the sound went away.