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I think the float in the tank(sending unit) may be stuck in the full position. If you can pull it out you should be able to check it. I really doubt it is the gauge since it does go from empty to full.
12v on the leads when diconnected does not sound strange to me at all, if you have a 12 v system and open the circuit you read source voltage if there is continuity back to the source because if there is no current flowing there is no voltage drop.
When you connect the leads to the sender you complete a circuit and the source voltage is divided between the gauge and the sender which are in series.
Trying to connect a lamp where your sending unit is probably will not be of much help.
If you get the sending unit out of the tank and diconnected, you should see the resistance of it change as the float is raised and lowered. Let us know how you make out. I pulled mine out once and it was pretty easy.
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