Hour Four: where it will keep
Nudge. The carving is a riddle about one of the parts on the joiner's bill. Which part stands at the foot of a stair and holds up the rail?
Harder
Treads, balusters, string and rail are all on the bill, and none of them is the post at the foot that holds the rail up. That post has its own name, and the bill gives it.
The answer
The word is newel.
The post at the foot of a stair, which carries the handrail, is the newel. This one's cap lifts off and it is hollow, as the carving says, and Pike's list of places to search does not include a stair.