Add a rule named “The Black Cat”:-

There is The Black Cat in the Banewood Mansion, whose Location (which is a Room) is privately tracked by the Narrator.

Whenever the Location of The Black Cat changes, the Narrator must reflect it on the Banewood Mansion page in the form of “The Black Cat is in X”, where X is:
* the name of the Room that is The Black Cat’s Location, if that Room is Lit, and there is at least one Explorer whose Location is that Room;
* “an unknown place”, otherwise.

Set the Location of The Black Cat to the Foyer, and add the string “The Black Cat is in Foyer” to the Banewood Mansion page.