best guess:
Congrats on finding
two AJAK motors! - :up -
I don't know if this is the exact switch, but it's similar to what you've got.
You can replace 'em if you break the metal extenders (which I wouldn't worry about).
See
Microswitches at the bottom of this page, for starters, but maybe buy from DigiKey?
I don't think the reeds are magnetized.
However, if you will remove the disc with the reed, so it's not close to the five magnets inside the housing, you can
try a demagnetizer.
You just don't want to zap the magnets by getting close to them!
If you replace the reed, be sure the new one is the same length.
I strongly suspect you get 10 clicks per revolution of the 5-magnet wheel.
How that happens, is by a magnet being under
either end of the switch.
Also, measure exactly where the old reed was located; you must put the new one in the same place, and aligned the same way, to work properly.
Ya don't need to use calipers and make blueprints; just be careful! -
For glue, you need something that'll stick to your disc, and encapsulate the reed.
Rough up the disc where you want to put the reed. That'll aid adhesion.
If RTV or silicon rubber will stick to the disc, that'd be my first choice.
It'll make for a reliable encapsulant of the reed and wires.
Look for the kind that's good for electrical connections, not the one that smells like vinegar.
There are other bonding agents, such as industrial adhesives you might have.
Elmer's makes
Ultimate Glue, an expensive and real strong polyurethane glue. It might work. Follow directions.
Then, Liquid Steel is an epoxy. I've never used it but read about it's success in many applications.
Just don't bother with that 1-second cyanoacrylate adhesive - it's crap IMO.