Yes, it's the same as on the original F-1 body. Picture the bigger lever having a tab inside that pushes on a tab on the mirror lockup... so as you push the lever from upright towards the lens, the tabs hit and it moves the mirror lockup mechanism. Now that long lever can actually flop around between the upright position and the mirror lock position, because the mirror lockup mechanism is already locked in place. Gravity typically keeps it pointing over towards the lens, that's all. However if you bring it back upright and then push it the other way, away from the lens, that little tab inside pushes on the tab of another mechanism - the self timer. It can go almost all the way to straight down for maximum self-time. Again, I think only gravity keeps it that way.
When you press the shutter button, the timer mechanism inside slowly circles back up, bringing the lever with it.
Oh, and to release the mirror lockup you have to release the aperture stop-down, which is the lower smaller lever. That's probably the part that is confusing you - it isn't like pushing the big lever towards the lens moves the mirror up, and pushing it back the other way pulls it down again; two different levers perform those two functions.
That's actually the one feature I sorely miss, having upgraded to the F-1 New: no mirror lockup.
Duncan