Sorry, the walkthrough I am looking at is now clear as to when you are no longer timed. It says this:
When you've solved the slider, you'll find another KEY. Take the key back to the parlor (where the lion head is) and use the key on the large cabinet standing left of the fireplace in the corner of the room. Remove the fake SCEPTER from the cabinet.
Return to the hallway and turn slowly to rest your eyes on the "fake statue" at the end of the hallway. You've got a couple of scepters now in your inventory that might look quite charming as an addition to that statue. Use them both now!
Maybe the timer doesn't end until you get to level 3, which begins right after the end of this.
And looking ahead at the walkthrough, there is at least one more timed sequence later on in the game.