A year or so ago...maybe a year and a half...I posted titled "Your fuel gauge explained, sort of." Here is a link:
https://tinyurl.com/mr32amapOn the back side of your fuel gauge, there is possibly a red tag. At least originally there was and it is important. Or maybe some prior owner labeled the two connections. On the back of one I used for study, etc I labeled it "red" and "fuel" to tell me the "fuel" side went off to the fuel sender unit. The red goes to the ignition switch. If you confuse the two, it is highly likely you will burn out your fuel gauge. In that post linked above, I try as much as possible to explain how the fuel gauge works...how it is a balanced magnetic scheme with two similar-looking but different electromagnets and how they both work to show you how much fuel you have. I explained this a week or so ago on another post. If you burned up your fuel gauge, you can repair it...that is if you are a very patient person. What must happen is you must separate the 2 electromagnets, buy two different gauges of magnet wire, unwrap the original coils, measure the length of each type of wire used and replace it, connecting the two as was originally done. What you have are 2 magnets, each wound with different wires so that they have different electromagnetic field properties. Sadly when an electromagnet is fried, there's not usually a good way to know where the boo-boo manifested itself...could have been easy to see, but usually is buried deep within the windings. Good luck. If questions, please let me know.