"but it's a BSA so I didn't expect it to....."
99.7% chance it's an electrical issue. Lucas was not called the Prince of Darkness for nothing.
https://www.hagerty.com/media/mainte...everyone-says/
Early this morning I was thinking about the motorcycles I have owned starting about 1967. All were Japanese except four: a Norton Atlas, a BSA Starfire, a Changjiang 750 sidecar and a genuine WW2 Zundap military sidecar. Plus my two recent Lifans. Probably about 20 Japanese bikes.