Turpentine and Lighter

Turpentine and lighter is one of the various small clue items found through out the various rooms in the hotel.

Spoilers:

Used in conversation with Amy to reveal that Jimmy used the items to burn her stuffed bear

It's also used in conversation with Rose after cross-referencing a plot point in the Lower Ground Floor to discover that Rose could no longer live with herself after telling Jimmy who his father was, pushing her to self-immolate.