I just bought a 98' Tahoe and the gas/fuel gauge does not work. Checked the fuses and tried a new one for the gauges fuse and the gauge worked but then went back to empty. When I removed the fuse the battery gauge quit working but works fine when the fuse is in. Why would replacing the fuse cause the fuel gauge to work then quit?

The computer does a sweep test everytime it senses power. Check it next time you turn the key to run the gages do a little self test. However the fuse and gage won't be your problem. They are very bad for the fuel level sensor in the tank getting corrupted or dirty and doesn't read properly. You can try to add port fuel injector cleaner to the tank, but problem will usually reoccur. You will need the fuel tank dropped and the level sensor replaced.

I would say that the fuel level sending unit is going bad and may have just briefly worked, on the other hand you may have a short in the wiring if it has either bounced you fuel level guage or has come on and cut out several times.

Sounds like the sending unit in the tank is bad.