Sometimes the wiper arm and shaft can shift and lift the contact point off the resistance wire. It shouldn't be that loose back and forth but it has happened.
Can you examine the windings? Are they intact. Can you put your meter on each end of the windings? I have carefully pried a few units open and repaired them with extremely small copper phone wire. The Ohm's value will change but the gauge will work again and not be that much different. If you have a clean break in the windings put a light drop of super glue on each side of the break. Using a nail file or very small piece of fine 500 or better sand paper very carefully clean the wire windings to prep for tinning. Carefully tin each side of the break and then make your jumper wire. Tin the ends and very carefully solder it over the break. It is important to keep all solder, flux, and glue out of the wipers path. that must be clean and debris free. You might test the tension on the wiper arm. To much will ruin the windings by wearing through. Just make sure it has light contact and cannot drift in the sending unit case removing contact. Test and reassemble. I did this to my Under seat tank in my CJ-5 15 years ago and it still works.
To test what you have put one lead on the screw terminal and the other lead on the frame of the sending unit. Move the arm slowly and the OHm's value should change. Don't touch the sending unit post while testing. Your skin will conduct and make a false reading.
If it's burnt from a bad hook up you will need a new one.
Liz, covid, murdered 10/19/21