Yeesh! This can be messy. A very common device from WW-II era was the "selsyn". These had a wound rotor and a stator wound just like a 3-phase motor. You connected some excitation (typically 120 V 60 Hz for Navy ship applications, and 26 V 400 Hz for aircraft applications)
to the rotor, and just connected the stator windings 1:1 together. If you mechanically drove one shaft to some position, the other unit would move to the same position. I think this could be a similar scheme, but with just two stator windings at 90 degree relationship.
This is commonly called a "control transformer" and is actually identical to what is now called a resover. If the rotor is excited, the stator windings produce a singla which is either in phase or 180 out of phase with the excitation, depending on shaft angle. Their amplitude varies as the sine and cosine of the shaft angle.
If you were to apply a sine wave that matches this relationship, it should work as a weak motor, enough to turn the instrument.
So, you need to convert the shaft angle you desire to sine and cosine, and then produce sine waves of that amplitude and 0 degrees or 180 degrees to the rotor excitation. Not a real simple thing to do.
Umm, one way to cheap out on this would be to rig a gear motor and pot or encoder to another of these motors, and use them like selsyns.
Your computer drives the gearmotor to desired angle, the sending selsyn sends the 2-phase output to the instrument which displays the right
position.
Jon