Both gauges, temp and fuel, and all three (oil) are supplied by the same power source, IE the IVR various names, intrument voltage limiter.
The electrical path is sender.....sender connector.........bulkhead connector.........to dash cluster harness connector.......board trace to the gauge stud/ nut..........through gauge unit........back out gauge stud/ nut and board trace..........to IVR.
Generally "the troubles" are
Bad sender, bad sender wire connector, bad terminals in the bulkhead connector, bad connection at the harness connector, bad connection at the PC board connector pin--to board trace-------bad/ burrned out trace, bad connection(s) at the gauge stud / nuts, bad gauge unit, and broken / burned board trace to the IVR.
Pull the bulkhead connector apart and check "that far" and if not................
Likely time to drop the column and pull the cluster