Take out your sending unit and take a voltmeter to it. I'd say that's your problem...just a guess though.
If it is, you can get another mustang sending unit pretty cheap. If you choose the easy mickey-mouse way... take one out of an old falcon or torino at your local junk yard. Check the tank size though and make sure it is the same volume as your mustang.
Heheh. The fuel gauge has absolutely no connection with whether the engine is running or not. Neither do fuel gauges have anything to do with with fuel pumps (in ANY car). On late model cars the senders happen to be mounted with the in-tank pumps but they aren't interconnected. Gas gauges work by one wire going to it which is a variable ground depending on the height of the float.
I'll assume you do have some fuel in the tank. Since the gauge at least has a slight amount of movement, I'll bet you have a bad float. Older floats tend to be little brass cans. When they get a pinhole in them they fill with fuel and of course, won't float. This happens a LOT. I've replaced at least 6 floats just on my personal vehicles. Newer floats are are sort of solid foam called nitrophyl which are immune to filling.
The fix is first to pull the sender out. Annoying and messy if you have much gas in the tank. It's a little tight to work in but I like to jack up the front of the car and put it on jackstands as high as I can. This makes the fuel go to the rear of the tank so less will spill out on you. Disconnect the fuel line and the wire. The sender is retained by a metal ring which much be turned with a hammer and punch then the whole unit lifts out of the tank. Use a BRASS punch or something, this is not an area where you want to risk making a spark. Once you have it out you can reconnect the wire and hold the unit up against the body of the car to ground it. Have a helper turn the key on and watch the gauge while you move the float arm. Lift it up and the gauge should slowly go to full. If it does then shake the float, you should be able easily tell if it's full of gas and likely your problem. You can buy new floats at most parts stores or a complete sending unit from various Mustang parts catalogs. If moving the arm doesn't work, disconnect the wire and ground it out on the car by itself. With a straight ground the gauge should go to full.
All that failing you either have bad wiring somewhere or a bad gauge. First double check your assistant does have the ignition "ON", that you are really getting good grounds, battery is connected, etc.
Personally I would start simple...go out back of the car, climb under it, and
1. Ensure the wire is connected to the sender at the back of the tank (mine is a push on and comes off all the time.
2. Wiggle wire where it is attached to ensure good solid connection (again something I have with mine....will look like its on its not)
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