A standard sender should ground through the unit. At full there should be least resistance. No ground would read empty.
First check is to remove the wire at the sender - the gauge should read zero (key on). If you ground the wire directly it should then read full.
Second check is to read 12V from end of sender wire to ground.
If the gauge doesn't go to zero with wire pulled it is a probable gauge failure or needle is stuck/fouled in the gauge. If the gauge does go to zero it is a faulty sender in the tank.
A mechanical sender is likely a coil of wire with a wiper. The higher the float goes in the tank the fewer coils the current passes through (less resistance) and the higher flow through the indicator. A short in the coils can occur such that at low levels the effect of the coil is negated by the short.
On the gauge side it is rare but possible to get a needle stick.