Rallye mirrors

I'm not sure on the rallye mirror part but if you want to give it a go on keeping your mirror from flopping around, give it a soak in laquer thinner in one of those small harbor freight magnetic dishes. That should loosen up the factory glue enough to be able to pop the mirror out easily without breaking it. Then you can put super glue on the pivot ball inside the mirror housing. That should give the mirror something to grip on to keep it from flopping around. Then glue the glass back on and you should be set.

This repair worked on my Duster's driver side mirror for a good 10 years before it started to loosen up again. Problem is that whatever newer adhesive I used doesn't loosen up with lacquer thinner so I'd need to break the glass or buy a new mirror to fix it.
Good place to start. If you f it up you can get a new mirror. My brand new driver remote mirror can be adjusted with my thumb.