Miss Whitney noted in Longest Trek that Gene actually wanted Rand to be to Kirk what Miss Kitty was to Marshall Dillon--the confidant, in a way that even Bones couldn't be. Bones and Jim talk man-to-man, Rand provides the feminine insight to Kirk. (For some reason, the writers didn't seem to take a liking to this--the only time we saw a hint of this was in "Balance of Terror", when Rand comes into Kirk's quarters and tries to cheer him up a bit.)
And of course, a lot of us must have read the notes by The Bird himself to the effect that Rand to have a "sister-brother" relationship with Spock, "...perhaps because beneath her swinging exterior is a motherly instinct for lonely men."
She was to be even more audacious towards Spock than Bones--again, feminine insight, seeing things another man wouldn't. Spock, amused, would respond in kind and guess at some of her secrets (definitely some "humor" here!).