The quick check is toi turn the key to the RUN (not start) position.
Using a short piece of wire, momentarily touch one end of the wire to the terminal marked "S" (sender) on the gauge. This terminal should have a pink wire on it.
Touch the other end of the wire to the ground terminal on the gauge. If the gauge has +12 volts and ground the needle should pop over to full. If it doesn't then it's time to break out the meter. Check for +12 volts on the "I" terminal. Make sure the ground terminal has a known good ground. If the gauge itself is working, then the sender or the pink wire has an issue.
Disconnect the pink wire. Set your meter to read resistance. Turn the key OFF. Measure the resistance of the pink wire to ground. Depending on how much fuel is in the tank you should read 240 ohms empty, 109 ohms 1/2, or 33 ohms full. Those readings can vary a bit. If the meter reads open circuit or way different than stated, then move to the sender and repeat the test you just performed. If the readings are correct at the sender, the wire has a problem. If the readings are the same as previously, the sender needs replacing (assuming the metal shell has a good ground).
