Per the haynes manual you can check a fuel sending unit with an ohmmeter when you remove it. Watch the voltage change by physically moving the fuel float. If its not smoothly changing then your sending unit is bad.
If it does report smooth changing voltage, then the problem is further up the connection to the dash. The dash itself has a lot going on that might not be reflecting the incoming data appropriately.
Does everything else otherwise function appropriately, like does it start and run or change fuel level as you drive?
It is possible the problem had nothing to do with your sending unit in the first place. Test the other connections in the circuit and look for bad/open grounds, bad wires, blown fuses, etc