The required 'synchros' are magslips and quite different to any regular synchronous motor, they are also quite different to what model aircraft folks know as servos.
I have some idea of how they work and I have a few in the shed (but that is in New Zealand!).
This is Madmodders and we should be able to design and make our own!

Anyway, this is how they work: There are two devices that are similar motor like devices which have a three phase field and a single phase on the armature. Both ends are the same, the three phases at one end are connected via 3 wires to the three phases at the other end. Both armatures are connected to an AC current.
The AC current in the armatures induces AC currents in the field windings phased according to the position of the armature. If they are free to move the two armatures will take up a position were the 3 phases at one end are in phase with the 3 phases at the other end. Therefore if you move one and the other is free to move it too will move the same amount.
Now then, Madmodder hat on!
A common or garden car alternator has a 3 phase stator and a single phase armature. In the alternator the armature is called the field. At first glance it would appear that two alternators could be used as a magslip link and drive the wind direction device.
Not really electronics, more electrics.
So, how to test the idea. Get two alternators that are similar. Get a low voltage AC transformer, those 12 volt lighting transformers might be good enough.
Open the alternators and snip out the diode bridge so that you have 6 wires coming from the stator windings. Use you meter to identify the ends that are connected to each coil then connect all three coils together in series, there will be 3 joins required and these joins are the 3 phase connections that you connect to the similar 3 phase points on the other alternator.
Get rid of the voltage regulator if it is internal and find the two wires that are connected to the rotor via carbon brushes (these will likely be labelled 'F' for field), connect the two rotors together in series and connect to your 12 volt transformer along with a 12 volt light socket all in series.
THAT'S IT!
Put a 12 volt globe in the light socket and turn on the power to your 12 volt transformer. Hopefully there will be a bit of buzzing and the light will be lit but not full brilliance. Turn one shaft and see if the other one moves, or at least shows any tendency to move.
Report your results.
BTW, these devices were invented in WWI and used in battleship range finders and gun control equipment. They wanted very low friction and maximum sensitivity and resolution so did away with the troublesome slip rings and brushes and replaced them with magnetic connections which they called magnetic slip rings, hence the name 'magslip'. They are called 'synchros' in the US.
There are a couple of reasons why this idea might not work and one of them is that the alternator may have too many poles, but I dont really know so hopefully some keen type will try the above experiment!