For the gauge just connect a flashlight batt to it, 1.5 volts, it should deflect to about one third of scale, full scale is about 5 volts

The part in the tank is a rheostat, a variable resistor. To test that you put an ohmmeter on it (preferably a good one) and look for some conductance. You should get consistently better conductance as the float rises. I don't recall the exact ohm values but I think it's about 50 to 70 ohms at full scale (I think, but not sure)