When you turn off your 1989 Camaro RS your fuel pump keeps running and kills your battery. What is the cause and the fix?

The '89 Camero RS has an electric fuel pump and a relay to operate it. The relay is "turned on" by the ignition system. When the key is turned to "start" or "run" the relay is energized. (The relay is used so it can be operated from the switch. The pump itself draws too much current for it to be practical to run the pump directly through the ignition switch.) Normally the relay will energize and close and then de-energize and open with the operation of the key (ignition switch). That starts and stops the fuel pump. But if the relay is stuck "on" (the contacts remain closed) then the switch will de-energize it but it will keep the fuel pump powered up. The relay may be mechanically stuck or the contacts may have gotten "welded shut" during operation. Either way, the relay is the primary suspect in this case. Good luck with your troubleshooting and repairs.