Facebook no longer allows a user to hide their account from a Facebook search, from what I can tell. They allow a user to hide their account from outside of Facebook, but not within. I've tested the privacy settings with two accounts, by doing a search from my other account, but got nothing to work. If someone knows how to do this or if Facebook is working on a fix, please answer this question.
Looks like Facebook used to have another option of "Friends" under this setting, but now it is gone.
"Who can look up your profile by name or contact info?"
- Friends of Friends
- Friends (now gone)