Sorry I'm a little late to the party here. Is it just the fuel gauge and temperature gauge? If so, then below could be the issue:
I have a factory manual for my 95 Mustang - I don't know if it's the same for your year, but I can't imagine it would be too different (though it might be, so it's worth finding one if you can).
According to my manual, the fuel gauge and temp gauge both share the same BATT input, and both share the same GROUND. So if it's those two gauges, then it could be either of those, probably bad ground as evilcw311 said. The fuel gauge also has the anti-slosh module but that doesn't affect the temp gauge, so I don't think it's that.
The ground, on my car, is located in the left side harness plug (there are two plugs, one on the left and one on the right). It is pin #2, and (again, in my car) it is Orange w/ Yellow stripe (O/Y). This wire splices into a Black w/ White stripe (B/W) wire, which terminates in an eye-ring bolted to the dash, down in the center console area near where the amp would be if you had one.
HOWEVER! This ground (the B/W one) is shared by other stuff, such as the radio. Does your radio work correctly or act weird as well? If your radio is fine, then the issue is most likely in the O/Y section of wire, and NOT in the B/W section.
Where the O/Y wire joins in to the B/W wire is near the Multifunction switch (the turn signal, wiper, etc. switch). That will probably suck trying to find that splice. What you want to do is, with the car running and the gauges *not* working, measure the O/Y wire's resistance to see if it's a good ground or an open circuit. If it's open, it's obviously your problem. (NOTE: I say the car running because the ground fault could be intermittent - you need to know that the gauges are currently not working before checking continuity and I can't think of any other way to do that without physically seeing the gauges not work). However, it might be hard to do this test so you can just assume it's bad, splice in your own ground wire to the O/Y wire, and run your new wire to a good known ground location and just be done with it. Also, you have checked the fuse and it's okay, yes?
Lastly, because the gauges seem to work initially, I am assuming the BATT wire is okay. And it is possible, however unlikely, that you got a second bad cluster. Do you know for a fact that your second cluster should work?
