This can be accomplished with variable restrictions for all the links. Basically, you just set a single variable (like TIME as an example) to 12. Have all the links restricted to work only if the player has more than 0 TIME. Each time the player clicks a link, reduce TIME by 1. This represents how much time you have left before the movies, and causes you to lose time as you visit each place. Once the player has clicked a link 12 times, they'll have run out of time, so the only place they can go to is the unrestricted link (the movies).
If you're not sure how to handle this, I'll look into it if you want, though I'm sure others who already know the code will pipe in before then.