Bosley’s recently sold a BM badge which I’d not seen before. It appears the overlay is held in place by a rivet.
https://www.regimentalbadges.com/en-...2#.YTe6DyV4UlR
I’ve read they were worn by Lighthouse keepers and staff as well as Petty officers and ratings on lighthouse tenders.
Ultimately a badge I’ve never seen anything definitive on and if ever genuine has been restruck from the original die in truly prodigious quantities. That the badge in the OP appears double struck from the reverse lettering does not bode well in my opinion.