Mark 2 is right. I've spent days in the archives and have extracted a full record of B&S engine sales. There is no separate sales record for engines and parts, it's a series of archive boxes containing every order; binoculars, range-finders, octophones and engines, but from that I have as complete an engine sales record as it is possible to get.
My bike, "Ever Onward" is a running machine in regular use, with a WA7, 500cc, engine.
Jagnut's engine, 23 1331 (it cannot be anything else) was despatched new on 21 June 1923 to Wallace, in Glasgow. Wallace made agricultural equipment, but I've never delved into the details of precisely what.
JFerg