RE: Newbie...Gas and temp gauge dont work
I got a 58 hardtop a year ago and went through the same problem.
First you need to understand how the circuits work. You have 12V from the switch. It goes to a votage regulator on the back of the instrument panel. This is not to be confused with the item in the charging system. It it is a bimetallic on off switch which essentially turns 12V into about 5.5 V (average) which is the power for the two gauges you mention. This should be replaced to be on the safe side (or verified to work OK with a multimeter). They are about 16 to 20 dollars. The 5.5 V Dc goes to both of your two gauges and then to the sending units for each. The sending units may be thought of as variable resistors. The fuel sending unit, for example, varies from about 78 ohms (Emtpy) to about 10 ohms (full). At the end, both ground out.
If the unit puts out 12VDC all the time it is closed and has probably fried your gauges.
The ground should be checked and cleaned up in both cases. While in my case the temp sending unit screwed into the front of the manifold (behind the water pump) in fact I had no ground. I got around this with a short jumper wire.
You can see if either gauge has potential to work by disconnecting the lead to the sending unit and BRIEFLY grounding it out. The gauge should jump right up to either Full or P (for Hot).
The tank sending unit (easy to get to in the trunk under a little
black cover) may have corrosion or gunk and not grounding out. Clean this up to be safe. Be careful here as you will be staring into the gas tank while doing this!!
So at this point you want to isolate the source of the problem(s)- voltage regulator, gauge, sending unit or ground . A multimeter is very useful as are jumper wires.
You can easily buy a new regulator or sending units. If your gauges need rebuilding, such services are available (see Hemmings). They are not expensive but are slow.
During the winter you might send the regulator, gauges and sending units as a group and have them recalibrated for accuracy.