If your 56 still has the original King Seely fuel gauge sender, I would be reluctant to replace it. These units are hard to find and if you can find one they usually sell for around $300. The King Seely operates on opening and closing contact points which send electrical pulses,which vary with the float level, to the gauge. The only after marketsenders I have seen send a steady electrical power, the amount which varies with the float level, to the gauge. The original gauge was not designed to work this way and while they will show a movement of the gauge needle, they are not at all accurate (Do a search on this forum and also the Ford Barn forum for many complaints on the aftermarket senders). It might be possible to fix your original sender if it is at fault. Carefully pop the cap off with a screwdriver and clean the clip where it makes contact with the inside of the cap when it's installed. Also clean the inside of the cap where it makes contact with the clip. While the cap is off, check the points. If you clean them, the sender might start working again.Finally, check the thin induction wire that wraps around the bi-metalic point arm. If it's broken, an auto electrical shop might be able to repair it. The first thing to do is make sure the sender is well grounded, as already suggested. If it were me, I would run a ground wire from one of the sender to tank mounting screws and connect the other end to the frame of the car. Scrape the frame so you see shinny metal where you attach the wire.
To test the gauge, hook up two 1.5 volt flashlight batteries with the two wires long enough to reach up under the dash to the two terminals on the back of the gauge. It doesn't matter which wire goes to which terminal. The steady 3 volts should cause the gauge to register ½tank.