The dealer will use a signal generator to diagnose the fuel sender which is in the fuel tank (can be accessed via a porthole in the trunk).
The resistance changes with the sender as the fuel level drops, a piece of debris or loose connection can affect the gage reading.
E 40 to 77ohms
1/4 129 ohms
1/2 165 ohms
3/4 204 ohms
full 233 to 250 ohms
Low fuel indicator On at 100 ohms
Low fuel indicator Off at 106 ohms
The only other thing that it could be is the instrument panel (fuel gage itself) and again the dealer will need the signal generator to diganose.
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