Oooh wait a second ! Update !
So in playing around with GarageBand, it seems like if you open the on-screen keyboard (Command+K keys), and leave the on-screen keyboard up then the instrument window stays open !
At least it works that way here.
Wow, you learn something new every day !
EDIT : Wait a second, now it's not working

!
Arrgghh, I don't know why it worked a minute ago.
Now I'm mad, I'm going to try to mess around with it tonight, and see if I can figure out why I got it to stay open that one time.
May be the sequence that I did it in, I will try to figure out what I did that one time if I can.
Sorry !
- Jay