If all else fails, I could write an AutoHotkey script to lockpick it.
Alright I brute forced the puzzle, and now I can see where the solution came from.
Turns out the zoomed in view of the clock you get is just for looks, it's not a hint.
The solution is sort of neat, but what frustrates me is that is that the items needed for it came off as a joke items that didn't do anything, like the calendar, unless that's also needed later.
I remember the mouse at the start saying something important about their suitcase, but I also thought it was just an odd joke. I suppose that's on me for not paying enough attention, but it would have been nice for that NPC to stay in the room, so that I could hear what he had to say again considering how important his hint is.
If I had dropped the game for a day or two and had forgotten what he had said, and only had a save where I had already entered the room, I'd have to replay the whole game to get that hint again.