If not heard running check the oil pressure switch for the 12 volts needed to run the fuel pump starts there on that harness. If it is stuck the pump could continue to run.
Why You Shouldn T Drive Around With Your Low Fuel Light On
Fuel pump keeps running with key on. That makes sense to me im going to try that tomorrow. Start the engine take off the fuel pump relay and leave the engine stop itself when this occurs turn off the key the you can take off the filter and changed it. Normally the fuel pump relay operates during starting and when turning off the engine. Once you located open the fuel door and take off the cap and leave it open. It wont turn off and it keeps running even with the key is off. Turn the key to the on position without starting the engine.
If everything works correctly key shuts motor off kill switch shuts motor off and fuel pump runs when its supposed to then its the alt. Replacing the fuel pump relay stops this from happening for a short time but it soon reoccurs. To do that first find the fuel pump relay in the main fuse box located in the engine. A full explanation of how the relay works and how to check it is quite long. 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. It sounds like you have a short to voltage somewhere.
Is it possible there is a short in the ignition system or is this a sign that the fuel pump is going out. If the pump runs with the relay removed its not the relay. I suggest you check the net for info on how a fuel pump relay works and conduct the electrical test. This primes the gas to the injectors when doing this. So i ran into a little problem with my return style fuel system. The fuel pump on my 1989 mercury grand marquis is still running after turning the ignition off causing the battery to drain.
You should hear the fuel pump running for 5 seconds if working.