The magnet idea is interesting, but if the stick was pretty much seated when it broke, the magnet may need to be real hefty in order to pull out the remainder of the stick.
The tranny pan on 126 cars is REAL simple to get off. Off the top, I forget if it's 12mm or 13mm. Put the front of the car on ramps. You do not need to go all the way up, just enough to provide crawl space underneath. The amt. depends on how large you are.
Block rear wheels with chocks to ensure car doesn't roll off.
Pull the tranny pan after 1st draining. 5mm allen head removes tranny pan drain plug.
The stick will be protruding some into the area where the fluid was. Push it upward. You may very well get it up enough so that it's now protruding out where it's inserted under the hood. Take pliers and pull it out.
Put pan and maybe new gasket on tranny pan - reinstall - do not over-torque the tranny pan bolts - 5/6 lbs. is all. Reinstall 5mm allen. You will have lost 3-3.5 qts approx.
While you're at it, you may as well replace the filter and if you really want to do it all, drain the converter too.
I suspect you're just trying to fish out the stick, so maybe the converter drain can be done later. Your choice.