The sending unit is typically a variable resistor and a float. Rather than using a voltage meter, you need to use an ohm meter and measure resistance with the float in full up and full down position. If they both read the same it is possible that dirt or grime is preventing a good connection with the variable resistor. Move the float up and down a few times and re-measure resistance. If up and down still read the same, you probably need a new sending unit.