At our NOAB, there was this one Training Development Officer there, a Major, who sat on the board along with all the Naval Reps. Now, she had this trick where, when she was asking questions, and taking notes on your responses, she would, while writing, stare directly into your eyes, without even taking a momentary glance down at her paper. Needless to say, pretty much everyone I talked to about it agreed that it was unnerving at best and freaky at worst.
I also have no idea whatsoever if the notes she was taking were in any way shape or form legible.
I can't say for sure, but I believe that one of the most important factors they look at when determining eligibility is watching how you interact with others, both your fellow candidates, your escorting staff, other sailors you meet, etc. Remember that the job of a naval officer is not dealing with the ship, the engines, the guns, etc. It's dealing with the people that is most important.