Try this......
"Rig" the sender connection however you must for electrical access. Alligator clip, etc. With the key "one" and the thing hooked up to operate "as normal" put your meter on low volts. Stab one probe hard into the sender ground IE any metal on the sender, and stab the other probe hard into a body ground point. You should read ZERO voltage. If not, it is not grounded
I believe you said you already tested the gauge for operation with a resistor. Did you connect your test resistor right at the tank connection? This will test all of the sender wire. If not, retest, and see if it still works. If so, and if the ground test above is good, it HAS to be a sender problem
You could double check by doing the following: Hook your meter up for current measurement, one probe hooked to sender, other probe connected to sender wire. If the fuel gauge does not read, check the multimeter, likely zero current. You can double check that by again connecting your test resistor, as sender wire---meter probe--through meter--meter probe--test resistor--ground, and you will see the meter reading.