fuel pump test wire

I am not familiar with this red wire, but you can achieve the same thing by jumping the relay and applying voltage to the circuit that powers the pump.

I am attaching the diagram below, but you need to remove the relay and jump B7 to F1. This is the command wire from the ECM to the power feed wire.

This will confirm your issue is the relay which is most likely. Here is a guide that will help with this:

https://www.2carpros.com/articles/how-to-check-an-electrical-relay-and-wiring-control-circuit

If your pump is not coming on and still does not come on when you do this the pump is the issue.

Please run through this info and let us know what you find, and we can go from there.

Thanks