I've had a couple of Mazda 626s, both with broken remotes. I got around it by making a little ring that sat in the recess where the two halves snapped together, but it didn't work that great and because I used metal, it limited the range. Dad recently showed me his remote, from an aftermarket keyless entry system for his truck. It has suffered a similar fate, but he had attempted to fix it with superglue. That didn't go so well, either. But his asking prompted me to make a new remote for him and me at the same time.
Started by taking a lot of measurements. Probably more than necessary for this, but I had what I needed. A height gauge is now on the list of things I "need". Other than that, the biggest problem I had was a coupler coming off of the X leadscrew, which prompted me to completely disassemble the mill and fix that. That led to me finding the bearing races had been replaced by common washers at some time, which was probably partly to blame for excess backlash in X. And while I had it apart, I found that the holes where the little screw that keeps the brass backlash nut in place were completely stripped out. So, I helicoiled them. And since I was this far into it, I figured I'd add a one-shot oil system.
I guess I should probably add some photos, maybe another thread on the way oiler, but I'll have to see if I got any good pictures when I was doing it. I did find that there are no articles about anybody else doing that to a sherline, or at least none that I could find. End result is that the mill is a much better machine than it was before and a much bigger joy to use.
Anyway, here are the pics of the remotes that I remade. They are both a little bigger, but the metal ring won't break off like the little plastic tab did.
Dad's remote. Old next to new.
Insides of both.
My remote. Old next to new.
Insides. A smarter person (and I think I became a smarter person as this project went along) would have used more tabs and a spoil board, like I did for Dad's remote, which I made after mine.