This is an interesting question and there are experts who could answer definitively, but it is amusing from an amateur's understanding to try to figure it out, so, I have a few ideas, in no particular order of most likely:
1. It is from a 1946-50 A7 that used a different breather path than later A7s and A10s (information courtesy of Roy Bacon, "BSA twins and Triples"). As I have a '55 A10, I don't know where the breather port in the timing cover occurs in the early A7s in relationship to the pin on the rotating breather.
2. It is from an A7 vs. an A10, which, having different strokes, may require different breather timing.
3. It might have been an experimental part that escaped the factory.
3. In Bill's photo, and on my partially diassembled engine, it is not clear as to whether the breather drive pin is relocated or if it is the puller holes that are relocated. The only rational I can think of for this would be a damaged casting form that was easier to modify than restore to original. (This is really remote.)
I would really be interested in knowing which, if any, of these theories is correct. The question made me consider the breather path in my A10 for the first time. On following the path I found the output on the drive side aiming down from below the cam bush housing. This then solved a small mystery regarding the oily mess on the outside of my drive side crankcase half. That mess seems to be one of the symptoms of the engine problem that brought on the current rebuild effort.