Kirsch pays little attention to the games room beyond ascertainig that it is empty; rather, having made sure to close its door, he heads straight for the library, granted, at a slower place than what he'd prefer so that Clytemnestra can keep up without exerting herself. He always felt at home among books, and that they managed to slip in here unattended is a welcome development, as well as an opportunity that might not present itself so comfortably later.
While it might be unlikely that they'll find anything truly revelative in the guest library, the lizard would rather ensure that it is not for a lack of trying, and he begins circling the room, methodically scanning the contents of the shelves.

Spoiler: OOC
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I'm not sure that it's designed for this kind of thing, but here's a Search check: (1d20+4)[18] (Kirsch is looking for historical accounts, anything that can give him a picture of the building phases of the castle, anything about the Conclave and anything that stands out/seems useful for trying to locate the entry point to the Tracery)
as well as a Knowledge (local): (1d20+7)[11] to see what Kirsch knows about how libraries usually arrange their books in millieus like this
with a Knowledge (architecture and engineering): (1d20+8)[21] for roughly the same, and to see if there's something unusual about the room.