What one finds at the top of those stairs is a bit puzzling. Did the Spanish have a swimming pool at the top of their fort? Of course there may have been some sort of structure up here, but if so, I haven't seen any mention of it. Could it be that this level served as the kind of "fighting top" one might find in a military ship of the days of sail, from whence musket fire could be poured down on attackers?

Yes, it could! This swimming pool is known as the Rifle Gallery.