Fuel pump runs continuos after shutting engine off

Ok. There is a company called, "The Fiero Factory" and has been in business for twenty years. Their website is: www.fierofactory.com and they have a "Tech" link at their website. Click on this "link" and it will re-direct you to the "question and answer" section. One of the questions submitted was exactly like yours, "...fuel pump stays on all the time even when I turn the ignition key to the "off" position..." Ok. This is being caused by a faulty or defective Oil Sending Unit, which is installed on the side of the engine block. It can be unplugged, unscrewed and replaced. It's function is to monitor the oil pressure in the engine when it is running. It is used as a "back-up" power feed to the electric fuel pump which is located withiin the gas tank. The gas tank is located in the transmission tunnel, between the passenger seats. Since the fiero is a mid-engined car, the transaxle (transmission) is located in the rear engine compartment. This leaves the space normally used for a transmission "empty" between the two passenger seats, and the GM Engineers decided to place the car's gas tank there to better balance the car's power to weight ratio, etc. If you ever need to replace the electric fuel pump, you will have to drop or remove the entire fuel tank. So, it is a good idea to understand where the tank is located. Replacing the electric fuel pump is a very big job and best left to a professional mechanic. When the ignition key is placed into the "run" position, the electric fuel pump is activated. You can often here it running for a few seconds and then it shuts off. This is normal operation, and it is pressurizing the fuel lines. It will turn back on once the engine starts running. It is the Oil Sending Unit that takes over the powering of the electric fuel pump from this point onwards. When the engine's oil pressure reaches 4 psi or greater, the Oil Sending Unit turns on and manages the power supply to the electric fuel pump. If the Oil Sending Unit becomes defective, it often keeps the fuel pump running even after the car's engine is shut off. Replacing the Oil Sending Unit should correct the problem. The remainder of the car's fuel management system is controlled by the onboard computer called, a PCM (Powertrain Control Modul) which is located behind the glove compartment box between the two passenger seats. Also, there is a diagnostic port for the PCM located beside the cigarette lighter. You have to remove the black, plastic bezel to access this port. To access the PCM, you have to remove the entire center console between the two passenger seats. Also, there are two retaining screws behind the glove compartment box door that must be removed as well, before access can be gaind. It is best to secure a Haynes or Chilton Repiar Manual for these tests and repairs. After the engine is started, the remainder of the fuel management system is controlled by the PCM and its associated sensors. The electric signal to the Throttle Body Injector (TBI) is controlled by the PCM and the PROM. If the PCM circuit board should become defective, it must be replaced. It will need to be sent to a repair and diagnostics center for testing and/or replacement. Good luck...