To troubleshoot a fuel pump problem on an '87 Corvette, you should first check the fuel pump relay. Its location varies slightly depending on the specific options on your car, but it's typically found in the underhood fuse box (also called the underhood power distribution center). The best way to find it is to consult your owner's manual or a wiring diagram specific to your 1987 Corvette. The relay is usually a square or rectangular component with several terminals.
If the relay is faulty, replacing it is often the solution. Testing the relay itself requires a multimeter. If the relay seems good, then you'll need to investigate further, checking the wiring harness and other components related to the fuel pump circuit.