Well. as you've removed the sender from the circuit and varied the resistance externally, it would appear that you are correct, the sender is faulty. Should be easy enough to remove it and discover that it is horribly clogged up and corroded.
But also check if the fuel gauge circuit uses a voltage stabiliser is the circuit. It is there to stop the fuel needle swinging about as the fuel in the tank swings about. They can be faulty and give spurious readings.
It will be a small alloy-bodied relay behind the dash.
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