Check for power and ground at the tank. If it is okay then the sending unit is most likely the cause.
on the side of the radiator
Yes.
your float could be stuck
1990 Chevrolet Lumina temperature sender is located on the back side of the thermostat housing. The sender has a wire that goes to the temperature gauge.
I had the same problem the fuel pump is more than likely on its way out
If the gas gauge stops working is there a fuse for it?
most likely the gauge
It's a GM
check ground first
More the likely the alternator has quite working are the belt / belts have broken on the front of the engine.
If your temperature gauge isn't working the problem is a bad gauge, grounded or disconnected wiring or, most likely, the temp sender isn't working.
bad temp sender usually. Bad gauge rarely.