The Mustang has a mechanical 5 voltage regulator for the gauges. This may be stuck closed putting out 12 volts at all times instead of an average of 5 volts needed for the gauges. That would be my first guess but could be a wiring issue.

TimC - send me a PM with your email address, I'll forward you the 66 wiring diagrams. 

Agree w/MS, the gauges for fuel, temp & oil pressure are fed from the CVU.  The fact that the fuel gage is ok and the amp gauge is pegged high is puzzling.  I'd start by removing the dash panel, and checking the wiring on it. 

Here is an update:

I finally got down to my nephews place and spent some time with him under the hood of his 66.  It has different symptoms than were initially reported to me.

Amp gauge stays smack dab in the middle like it has for the 15 years he has owned the car.  Probably non-functional.  We did not spend time on it.

Oil pressure gauge pegs high as soon as key is in "on" position.  We removed the gauge feed wire from the sending unit an gauge pegs low.  When I ground the gauge feed wire it pegs high.  Seems that gauge is operable.  We'll order a sending unit and swap that out.

Temp gauge starts low and climbs higher as we drive.  Based upon the bearing noise I hear from the water pump, I now presume the gauge may be accurate.  I forgot my infrared thermometer so I could not verify temps.  I'll bring my thermometer when we swap out the pump and thermostat.

Bearing Bob wrote:

What about the cardboard washers?

Since he found the problem wt the oil pressure sender end, it is likely bad, or wrong, sensor.

TimC wrote:

Here is an update:

Amp gauge stays smack dab in the middle like it has for the 15 years he has owned the car.  Probably non-functional.  We did not spend time on it.

Those Amp gauges never worked that well anyway.  IMO not worth repairing.  Suggest a voltmeter to replace it.
Here's a Ammeter to Voltmeter conversion that is available:
https://www.rccinnovations.com/index.php?show=menu-mustang-all#volts