Gas gauge woes..

After preforming the test above to see if the gauge and wire is working, get a battery jumper cable and clamp one side to the fuel tank along the seam. Make certain it is a good connection. Clamp the other side to a good ground. If THAT makes the gauge work, then your fuel tank ground is not good enough.
If that's the case, sometimes a copper wire and two hose clamps on the fuel line works better than the factory "clip" ground.