I can kind of re-seat it and it works but it’s still very loose and sometimes comes up with my finger. Is there a way to get it back to being more permanently attached without screwing it up?
Your trackpoint module is probably broken. Please take a sharp photo of its inside with the red metallic part out of the way.
Yes, it does. Please use silicone glue to glue the stem back and then let it dry. It should work afterward.
Thanks. I opened up the module, there’s a green square stick (pictured above) surrounded by a circular metal plate. Is there any of that I need to be careful not to get glue on?
To be safe, it’s better to get glue only on the surfaces in contact with each other.
I would recommend looking into one of the gel forms of cyanoacrylate (aka super glue).
Being a gel they’re much easier to apply precisely to a small area.
Remember that less is more with this stuff, as it bonds extremely well so just the tiniest of drops is enough.
I’ve personally used this one to repair a number of things:
https://www.amazon.com/dp/B0006HUJCQ