Wait a minute! Aftermarket gauges can be your friend. I use a set as a redundancy measure and because they are calibrated with actual numerical markings. Plus the PO already chopped the dash for them and it was easier to fix them than fix the dash.
I forgot to say to trace the yellow wire starting at the cluster since you said it's still there. It should lead to the sender but maybe it went bad and was bypassed by the one you found. The original question still stands then...where does your loose non-factory sender wire connect at the gauge? On one of the studs?
Also, with the cluster connector still connected and the battery hooked back up, you can (*) use a piece of wire jammed into the connector at the yellow wire connection and short the other end to ground to test the gauge. Aha! Shorting the sender end before didn't do anything at the gauge because it isn't hooked up there. See where I'm going? The yellow wire in the harness might have gone bad and been bypassed but we don't know where along the wire it's bad. We don't even know if the ring connector on the loose wire was ever hooked up to anything. If this (*) test works, you can try to splice the loose wire a few inches from the cluster connector or remove the original yellow wire from the cluster and replace with the loose one.