Sporadic voltage at fuel pump relay coil

This sounds like a fuel pump balance module is going out, here are wiring diagrams to show you how the system works with the location of the module which is on the frame rail next to the transmission on the driver's side. Check out the diagrams (below). Let us know what happens and please upload pictures or videos of the problem.

Does the engine crank over? It sounds like low voltage. If you remove the wire from the pump does the relay, still make that noise? You may have a fuel pump that is locked up.

There is a ground wire by the thermostat, can make sure it is clean and tight? Also try to unplug the oil pressure sender at the rear of the engine near the distributor. Maybe the PCM is not supplying the correct voltage to the fuel pump relay.

Yep, that was my next suggestion, here is the location and how to replace it.

When replacing a production ECM with a service ECM, transfer the broadcast code and production number from the production unit to the service unit. Also, during replacement, the PROM, and if equipped, the CALPAK must be removed from the ECM being replaced and transferred to the new unit. Refer to "PROM, REPLACE" and "CALPAK, REPLACE" for procedure.

1. Disconnect battery ground cable.
2. Remove right side kick panel, then disconnect the two ECM electrical connectors.
3. Remove ECM mounting hardware.
4. Remove ECM from passenger compartment.
5. Reverse procedure to install.

Check out the diagrams (below). Please let us know what you find.

Let me know, have a good weekend.