Crazy fuel gauge problem (long post)

The only thing left is what all is common to the fuel gauge. That is, the wiring and the fuel sender, and the gauge itself. I would find/ get some substitute resistors to hook up to the sender wire, and see what that gets you. If nothing changes, "one last thing" would be to pull cluster and check connections to the gauge, follow the path. Follow from the IVR to the gauge, make sure the gauge studs are tight, follow back to the harness connector, and then check out the sender wires.

If that is all OK, there is only one thing left and that is the gauge itself.