Fuel gauge is usually the sending unit. The temperature gauge also. If you want to do a quick test, find the temp sender on the engine. It will be the one with the single wire going to it, not the one with the two wires going to it. Once you find it, get a helper and turn the key to run but do not start the engine. Take the wire off the sending unit and ground it to something metal on the engine. The gauge should read full scale to one side. Then take the wire off the metal and let it hang in the air. The gauge should swing full scale the opposite way. If it passes this test, the wire and the gauge are good, the sending unit is bad.
You can do this same test for the fuel gauge if you want to crawl under there and disconnect it from the tank. And pick the proper wire, one of them feeds the fuel pump. I think the proper wire may be yellow/white but not sure on that.