there is a yellow wire that runs all the way from the sender, to the instrument cluster.
grab your multi-meter, set it to ohms, touch one side to ground, and the other to the yellow wire. it should read 16ohms empty, and 158ohms full. with an even spread between them, (i.e. 87ohms for 1/2 tank, 51.5ohms for 1/4 tank etc.)
go put a few gallons in the tank, and see if it changes, if it changes, and the gauge doesn't, you have a bad gauge, if it doesn't change, the sender is bad, either the potentiometer inside it, or a float issue