I’m not descending into madness because mount and unmount icons make no sense

An icon is a "visual shorthand" that lets your eye, within a few miliseconds, glance at a button you've used before and think sub-conciously "i am clicking the right thing". What matters more than "correctness" is unique-ness, and both Play and Stop are giving the OP feelings of madness because they are strongly tied to other concepts in their brain.

Mounting and unmounting (to my simple mind) mean making the physical hardware, which may be connected, available to the OS. So.. off the top of my head here... something like a disk connected to a folder, and a disk with the connection to a folder broken or dotted - might work.