The commonest cause of this is goop building up on the inside wall of the tank and connecting the probes together. Problems with the resistor pack are pretty rare.
The resistor pack is simply wired with resistors in series, connected between successive probe leads. Thus, there's one between "empty" (really the ground return) and "one-third", one between "one-third" and "two-thirds", and another between "two-thrids" and "full". I think, but don't know for sure, that the resistors are probably all the same nominal value, so the resistance between "full" and "empty" should probably be three times that between "empty" and "one-third".
The sensor system works by having the fluid in the tank more or less short out one or more of the resistors, which alters the overall resistance of the unit and is detected by the readout display unit. It's not very sophisticated or liable to electrical problems beyond things like broken wires etc.