Fuel Pump Rewiring

I would not worry yet about tracing the wiring. It sounds like someone hacked it up. So, the relay and ECM being corroded sounds like a possible better issue to start with.

What I would do is go to the fuel pump and check the voltage on the black/pink wire or the gray wire if they ran it straight to the pump and use the black wire as the ground.

Here is a guide that will help with this:

https://www.2carpros.com/articles/how-to-check-wiring

When the key is on there should be 12 volts on this wire.

If there is not, then switch to a known good ground and check for 12 volts again. If you now have 12 volts then the wire is not the issue, it is a ground.

However, if you still don't have 12 volts then you need to go back to the inertia switch and check for it there (assuming they didn't bypass that as well). Then go back to the relay and check for the voltage there.

If they are corroded, then we may have found the issue.

Please let us know what questions you have.

Thanks