You just have to keep the 'use' key pressed, making sure you're oriented so you can see Jan as she sprints ahead and hits the next switch. *THEN* you can release.
I wonder if your focus is moving off of the switch - that would be the same as releasing the button.
It seems tricky at first, but I just completed my 2nd anniversary run-through, and that took me ~10 seconds from detention to the hanger.
Dopelar effect (n.) The tendency of stupid ideas to seem smarter when they come at you rapidly.