Uhh theres no time limit, you just need to wait for your clock hands and your gears to finish
Also if you couldn't click its either because you were on the tutorial or the round finished.
Huh! I'm not sure why, but refreshing the page seemed to fix all the issues for me. I can now play properly.
Okay, I figured it out. In full screen mode, only the very top portion of the "forward time" button is clickable. Playing not in full screen makes the game work exactly as intended.
Ahh unfortunate