Truck Repair: Fuel pump, oil pressure switch, engine oil pressure

Question
I have a 1989 GMC pickup that has a problem with the fuel pump wanting to run with the key switch off.  Can unplug the fuel relay on the fire wall and the pump will continue to run.  Only way to stop the pump now is take the battery cable off or pull the fuse on the firewall for the pump.  I have had problems for the last 6 months with the pump.  Would park the truck over night and come back in the morning and the pump would be running. At that time if it was started and run for awhile and shut off the pump would cease to run--now it wants to run all the time. This though would not happen every morning and sometimes not happen for a week or two and then just happen for no apparent reason.
If you have some ideas let me know I can't figure how that pump is running with the relay being unplugged.  

Thanks

Answer
Hi Mack,
The pump is operated by the relay, which should operate it for three seconds when the key is turned to run, then shut off. If there is a crank signal, the relay will keep the pump running till there is no longer a crank signal, which means when you turn it off.
There is a backup system to run the pump also. This system is an oil pressure switch. Whenever engine oil pressure is present, that switch will run the pump.
My guess is you have a bad oil pressure switch, which is maintaining contact.
It is located behind the distributor, and is also the oil pressure sender, although that is a different set of wires.
Good luck,
Van