Good news, I think? Can't you trace by color? Don't remember anyone saying gauge should go to hot with key on. Just during a grounding test.
Just to be sure about wording....continuity is between the ends of a wire when it's disconnected at both ends. There are no terminals involved. You are just testing a wire. (you said "terminals of the sender wire"). Sorry to be so ridiculous sounding, in my former life the wrong meaning can cause all manner of chaos and going down the wrong paths during troubleshooting. Conveying by posting is a tricky business sometimes.
The sender wire could go thru a connector or two, I guess, on it's way. In other words, not a continuous wire. If that is the case, test each continuous wire that makes up the path. Start at the sender end (disconnected) and follow wire to the connector. Unplug the connector and see if there is continuity to the connector pin that wire goes to. If you get continuity, leave connector apart, check continuity between the mating pin and to next connector, if any, or to the disconnected end at gauge. Loss of continuity can be a miswire or connector not making contact. Just don't include any components in the test except connectors. When you find loss continuity, you will discover the problem.
Yes I believe you have proven that the gauge is good, the sender is good, but the sender wire is not. Just don't get fooled, like using a different 12V wire on that last test. Hope you used the wire that was part of the harness.
Very good work do far. This is what it takes, unfortunately. It's what is making you an expert. It's really rewarding to find and fix a problem. It's why a mechanic is worth his/her fee. No OBD on these trucks. Isolation, testing, elimination and deduction.
