I saw one of those sleeve devises that your asking about when I was a kid. My uncle had one, only it didn't pop out, you sort of drew it out. There was a line that you attached to a coat button / pin/ring--the line ran around your neck, under your right arm, and down the sleeve, it went through a ring near your wrist, and attached to the slide back up near your elbow. To make it work you unlocked it with your left hand somewhere near your right elbow, and then pulled the button, lapel pin etc, with your left hand--that made the slide go forward sliding the small gun into your hand. A light spring was attached to the slide making /helping it slide back up your sleeve. You did need to wear a shirt with loose fitting sleeves though.
If I remember correctly--my uncle carried a switch blade instead of a gun in his--but then it has been 50 years ago that I saw it, he may have been able to carry either a gun or a knife in it.
Cybin