The problem is the gas gauge keeps bouncing around. The cause will determine how it acts. Does it go intermittently to "full"? Does it go to "empty"? Does the "Low Fuel" light turn on?

The cause could be a bad connection on the float on the sending unit in the tank. The wire going to the sending unit could be rubbed through and grounding out. It could have a corroded connection. There could be a problem in the Body Computer that wire goes to or there could be a problem on the instrument cluster which is also a computer module.

If you have the overhead unit that displays "miles to empty" and "miles per gallon", see if those readings suddenly change. If they remain steady, the sending unit in the tank is okay. If those readings change drastically, the cause COULD be the sending unit, but it could also be any of those other things.