Great that all your EL lighting works. Thats usually not the case.. The speedometer is indeed a totally mechanical device, driven from the transmission with rotation sent up the mechanical cable to the rear of the speedometer gauge. To narrow down the issue, you would need to disconnect the speedo cable at the rear of the gauge , take a drive and see if you get rotation on the innards of that speedo cable from the tranny. If not, problem is likely in the tranny. If you get rotation, it's likely a defective speedo indicator gauge.
In a 66, the tach sender is a 4" round can with screw terminals, located under/near/behind the dash glove box. In an un-molested car the open-closing cycles of the mechanical points from the 12 V. side of the ignition coil goes to the sender can which translates those pulses to a variable signal sent to the tach indicator gauge. Problem here could be associated wiring, defective tach sender can, or a bad tach indicator gauge.
In these cars, the oil pressure, temperature and fuel gauges all operate off the output of a 5 Volt MECHANICAL thermal regulator device, which for a stock un-molested car is located INSIDE the fuel gauge. One terminal of those 3 gauges mentioned is sent a full 12 volts on startup for a few seconds to get the gauges moving. Once the car is running for a few seconds, the voltage to the 3 gauges changes to a slowly pulsating approximate +5 volt DC potential. The other terminal of those gauges goes to the respective senders which provide a variable resistance to chassis ground (- 12 VDC ). Again, you could have a wiring issue or defective regulator. If you disconnect the respective sender and short to the sender wire to ground MOMENTARILY, respective gauge should show maximum deflection.
A defective 5 V regulator can burn up / damage the coils in one or all of the 3 gauges mentioned. Interesting that the gas gauge is at full, is your tank full ? If you disconnect the wire at the tank sender, the gas gauge should indicate to totally empty. You need to narrow down what the cause of the problem is. Schematics and a service manual is a big help. Reproduced manuals are available on E bay. Retrofittable solid state regulators and tach senders are available here :
MOPAR Products Good luck with it..