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I think the problem is more likely at the tank... If I remember right you can pull the harness at the tank and ground the side from the tank. If the gauge moves then its not the gauge... I'm new here too but I am sure someone else will chime in if I am wrong.
There is a plug that carries all the wires to operate your instrument cluster except the mechanical speedometer. I have had trucks that for whatever reason was only plugged in partway only catching some of the circuits. If it is plugged all the way in check the printed circuit board for bad spots. I found this site when I was researching a gas gauge issue over 2700 posts ago. Mine ended up a bad circuit board. My gas gauge would work except when I pulled on the lights. If I dimmed the dash lights all the way to off the gauge worked. I could see anything wrong with it but I bought a used one from the pick and pull and that was it. I then put back in to the used cluster all my gauges and speedometer and the used one came with a clock...
Just noticed...is the gauge supposed to read all the time? Even with the key out, the gauge reads what the tank has in it.