There is a spring that pushes him up that is often worn or broken. There's also a smaller solenoid that pulls in a latch plate, if that's not working correctly the mech won't pop up. There's a few pictures of the mech here, https://pinside.com/pinball/forum/topic/south-park-club-come-on-in/page/8#post-4277837.
It might also have been disabled in the menu by a previous owner if it was malfunctioning
You can also find the manual on ipdb.