Update from nov 7 2018 we were able to bypass the fuse by running a bypass line purchased online at. I had exactly your problem and it happened to be on a 1987 ltd crown vic i had a very similar car.
Fuel Pump Relay Cut Off Switch Easy Fix 2001 2005 Hyundai Sante Fe
Fuel pump keeps running key off. A full explanation of how the relay works and how to check it is quite long. If this shuts off the pump the relay is sticking. See the diagram below and you will see that over to top left the oil pressure switch bypasses the fuel pump relay wiring diagram updated with tsb 86 65 02. If it is shorted out it ill bypass the fuel pump relay and basically supply 12 volts to the pump through the ecm fuse. The fuel pump is draining the battery. The ecm fuse is hot at all time 12 volts with key off.
Try rapping on the fuel pump relay with the handle of a screwdriver or similar. It runs for 5 seconds then it shuts off unless the engine starts. Also reset the inertia switch in case it tripped. Inside the relay has a set of points that opens and closes and what happens is the points get carbon on the surface and they stick together. Every electric motor in a car has a relay and a relay is nothing but a switch to turn the fuel pump motor off and on. Suspect the fuel pump relay.
If it is stuck the pump could continue to run. The pcm activates the fuel pump relay that turns on the fuel pump with key on. Thats when you smack it then it opens the points and shuts off the fuel pump. Can you hear the pump run hum in th fuel tank when key is turned on. Normally the fuel pump relay operates during starting and when turning off the engine. Fuel pump is running even when the vehicle is off.
Gallery of Fuel Pump Keeps Running Key Off
