Or maybe even the wrong stem for the case. I would use Loctite, and I guess as Hector suggests red would be better then blue. It's really made for this job and it gives you more time to work and clean up than CA does - so you don't end up gluing the whole assembly to your own thumb because a lot of glue is going to squeeze out and immediately dry onto the stem. Red Loctite should hold it very firmly but you can wipe it away before it becomes a problem.

Does the stem sit proud of the case as it needs to protrude to be fixed back in the crown, if not then it's broken.

I've learnt something new, didn't know the stems were friction fitted.  Love this forum.

As @mbwatch said, Timex crowns are friction fitted. It probably came loose from age, corrosion and/or abuse.  I would use red Loctite and leave it for 24hrs to reach full strength.

Sorry I don't have a pic of the other side and this stem is ridiculously difficult to get out so I don't want to do it again 😄 The other end is what goes into the movement itself. It has a squared end if I recall plus some small collars along the stem.    This is wonderfully helpful thank you! So obviously the grooves still work as I can wind it so that is good. If this was your watch, and it was more of a practice piece rather than a sentimental piece, would you loctite or CA it? I know loctite is removable but i've never used it in an application where force is being applied away from the threads (groves in this case) versus stopping a nut etc from moving on a bolt or threaded rod. In my layman common sense, I would lean towards an application of CA but in the world of fine watch repair, perhaps this is the last resort rather than first choice? One other question I just realized if I was to glue the stem back, I would image that the stem would but pushed all the back into the crown and not be floating with space left in the hole with the stem enters the crown right? I ask because the crown sits flush with the case so any miss regarding that would have consequences.