Thank you so much for playing and the feedback. It's very helpful!
The time does get used but it's only after you're done with the witness testimonies unfortunately.
I'm sorry about the cryptic puzzle and the frustration it caused. I would really appreciate it if you told me where you got stuck. It would help me improve it in a future version. Maybe I should have added better hints in the game. I know there are a lot of games to play in this jam but in case you're still interested in continuing, I've added images of the solution to the cryptic puzzle to make it easier.