Hi, I am a professional certified mechanic, with an engineering background, and 35+ years experience. I will do my best to assist you. Also keep in mind I don't know if you are a pro or a novice, so feel free to add any additional info at any time.
It has been over 20 years since I have worked on one of these, but I do remember them. You need to determine if the problem is with the fuel gauge or the sending unit in the fuel tank. Basically the fuel gauge is an ohmmeter reading the resistance of the sending unit in the fuel tank. The sending unit is a variable resistor attached to a float that moves up and down with the fuel level. When this system acts up you can start by either checking the sending unit or by checking the fuel gauge. To get into this you need to understand the relationship between the two parts, that I just described, and know the operating resistance of the system. The sending unit should read 12 ohms full, and 88 ohms empty. So you can either get some resistors and attach them to the gauge wire going to the sending unit to see if the gauge responds correctly to 12 then 88 ohms of resistance, or you can measure the actual ohms of resistance of the sending unit with an ohmmeter. I like to check both looking for problems. The vast majority of the times there will only be one problem, like a bad sending unit, or a bad instrument. Occasionally there will be a bad electrical connection causing a problem, so keep an eye out for that. Because the sending unit is very dynamic, and exposed to gasoline it tends to wear, so the majority of the times when there is a problem, the sending unit will be what needs to be replaced. Still it is a very good idea to test the parts, to be sure. Go over all of this and if you have any more questions at all, I am here to help. Good luck with it, have a great day, and Thanks for using Just Answer.
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