I would like to note that the relay will only activate for 2 seconds. The Fuel Pump Relay is energized for 2 seconds after the ignition switch is turned to “RUN” or as long as the ECM senses ignition pulses. So if the battery voltage is there for the initial 2 seconds and then is lost, this is normal. You may need to look at why the ECM is not getting engine pulse signal. Check the fuses and wiring if you are not getting battery voltage for the initial 2 seconds.
1993 Cadillac Fleetwood Fuel Pump Wiring Diagram