If there's no obvious lock, I'd say whatever it opens, it must be somewhere well-hidden, secret or of difficult access. Somewhere exclusive, maybe. The clock tower would track, at least, since I'm not allowed too deep or too high into the tower, and even the winding of the base gears is done with constant supervision. But if I get to see the key, I can at least pay more attention to any locks I see while I'm closer to it. Shot in the dark, maybe, but you never know.
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