Tom, as scoot suggests, try to fix it - nothing to lose. If your car qualifies for the new type sender/gauge set, the gauge is likely to be the new one (unless some PO replaced the gauge or the whole cluster in the past). If you see resistance lower, it may mean the float does not go down fully - maybe it sticks inside the tube.
I had a case last March with my W463 - indication empty, tank half full of gas. I had to clean and tighten the nuts on the wire lugs.
Some clue here is the reserve light - it is a separate circuit.