Do you have a copy of the Vulcan B Mk.2 Aircrew Manual (AP 101B-1902-15)?
If not, Peter Gill at FlightManualsOnline is a very reasonably priced source of scans.
Chapter 12 of that manual gives a good outline of the Military Flight System (by Smiths) including the Director Horizon and Beam Compass.
It also references RAF manual 112C-0800-1B Automatic Pilot Mk 10 B/C, which you may be able to find on line. It may be too obscure to have been scanned, though, in which case you could ask RAF Hendon Museum, RAF Cosford Museum or BAE Systems Heritage at Farnborough, and plan a visit to the UK ...
Are you in touch with the Vulcan Simulator project here? I can't post a URL, but they have a Facebook page and have been modifying real instruments to operate as simulator instruments.
Otherwise it depends what you need to know. I have more information on the civilian version, the Smiths Flight System, including civilian Director Horizon and Beam Compass instruments. It has many similarities, but, crucially, the Director Horizon instrument was different.
Guy.