I don't know much about them but a BSA hub gear is a totally different hub from an SA. It was considered superior as there is no neutral position and generally engineered to a higher standard.
Unfortunately the BSA hub factory was bombed during the war and production never re-started. It would be difficult to find bits for one.
It sounds like you have the indicator rod that screws into the hub? If so, you can find some way of attaching a cable to it. If not, I'm not sure where you'd get one.
EBay or someone in the V-CC.
Post a clear picture of what you do have.