There are two different systems in use for these sorts of things
'Synchros' work on a three-phase system
and 'Resolvers' work on a two phase system.
As key words, you'll find a lot on each in wikipedia etc. and you'll need to do some background reading on each.
The systems aren't necessarily servos, because servos are normally taken to mean the presence of motors with feedback systems. Synchros and resolvers can be used in the feedback arrangement of a servo system, but they are also used open-loop as usefully accurate indicators.
If you contacted Smiths, there is the possibility that you might get passed to someone who would help, but most likely in any large formal large business, it would come to official attention and someone would have to estimate the time and cost to formulate a reply. After smelling salts had been administered to the accountants, a terribly nicely written 'terribly sorry, but' reply would be written. The following month would be taken by people calculating the cost of that reply, and by people calculating the cost of that calculation.... ad inf.
Anyway, a lot of what you need to know is out there and freely available. It'll be in general terms rather than specific to your unit, so you first need to understand the general systems, and then see how your unit fits in.
Analog Devices make synchro/resolver to digital interface chips at prices that will scare you.
https://en.wikipedia.org/wiki/Synchro
https://en.wikipedia.org/wiki/Resolver_(electrical)
The two systems are rotary transformers using a polyphase connection so that direction is not ambiguous. Rotating one causes others to move in sympathy. Accuracy down to a degree is possible so they get used in aircraft for relaying the movements of gyro compasses, attitude gyros, flap positions etc. Warships used them for gun laying, compass repeaters etc.
Your two control windings suggest it is a 'resolver' rather than a synchro, but a lot of the understanding of resolvers is explained as an addition to synchros which came first. Read both, it will be clearer.
david