Ok, cool. Good to know. It is likely that the electrical on your fuel sender is okay. My guess is that the floating part inside the sender is stuck in some way. You are right, it is just a contraption with a floating piece inside that rises and falls depending on how much gas is in the tank (or how big the hill is you're driving up!).
If you access the fuel sender, you can take it out and inspect.
1) Empty your trunk
2) Remove the carpeted board from the trunk
3) Remove the spare tire
4) Under the spot where the spare tire was, you should see an access hatch. It is an odd shape and follows the contour of the round depression along the edge nearest the windshield. You need to be able to remove that hatch, which if you are lucky and someone has already worked on this in the past, could be just a set of screws holding it in place. It could be riveted in there too. Get to this step and report back if it looks strange or you're not quite sure how to get in there.
5) Once you have the hatch removed, you will see the top of the front of the tank. It is somewhat triangular and you are looking at the wide side of the triangle. You'll see the fuel pump boot/hoses on the passenger side, and beside it on the drivers side will be a smaller hole which has the fuel sender stuck in it. The wiring connections are on top, so check those while you're looking at them.
6) You can disconnect the fuel sender carefully from the wiring quick connect, and then loosen the retaining ring/clamp holding it in place. It is pretty straight forward. It is threaded, so you should be able to "lefty loosey" it and then pull it straight up. Don't get fuel all over yourself, but once you have it out, you should be able to tip it up and down type thing to get a feel whether the inside sliding/floating piece is stuck or not.
The fuel sender is supposed to be in there pretty snug with a gasket preventing fumes from escaping. Be conscious of that gasket material as you pull it out as you'll have to put it back when you go to reinstall it.
Try that and see what you find...
EDIT: and actually, once you have access in there, you can play a bit with what you see on the gauge while you're progressing. If you disconnect the sender, and then go to turn your car key to accessories, you should see the fuel needle go to 12 o'clock. Along those same lines, if you have it still connected to the wiring, but you take the sender out and tip it up and down, you should see the fuel needle move, so long as the floating piece in the sender is moving. This would also be a good time to see if your "idiot" light saying your fuel tank is low comes on. It is orange (or red maybe?) and the warning light is on the right side of the instrument cluster. You'll need a helper to do this with unless you have REALLY long arms!