This pic shows that the mirror attaches to the boom through a clever ball joint that allows both rotation around the mirror’s long axis and a slight amount of tilt. Unfortunately, after a few years, the ball stem breaks and at least one of the socket petals snaps. It’s a nice plastic design that’s totally unsuited to a few years of more-or-less daily bicycle travel.
The repair was easy enough, particularly because I think the boom has enough adjustment range to handle the job on its own (and I don’t care about how it looks). I filed off the stem stub and milled a slot for a 2-56 machine screw along the back edge.
Then you just slide a brass tube from the cutoff box over the end of the boom around some JB Weld epoxy, shove the screw into the blob, align the mirror with the boom, and let it cure.
Although it’s not shown here, the helmet attachment is aligned with the mirror at right angles to the helmet bracket. That puts it in roughly the proper position with the boom bent as usual.
I don’t actually plan to use this one for anything, but if I need a somewhat scuffed mirror in a pinch, well, it’s in the box!