Can a female have a high and tight?

Yes, just don't be offended when people mistake you as a male.

SSG (Join to see)
They can, but I think it goes against any standard reading of the regulation, at least for the Army.

It is considered an "eccentric" hair style for females

Good question, I tend to think not, sorta radish if you'd ask me

Can she? Sure. Should she? That's a different question altogether. The word 'can' denotes ability or permission, while 'should' is more qualitative. The high and tight is a decidedly masculine style, while long hair pulled tight in a bun is feminine. Therefore doing so may be construed as eccentric and against regulations. If there is no policy barring women servicemembers from getting a high and tight the decision is up to the individual. It must be noted, as Cpt Glover stated, that such a choice will erode the intrinsic femininity of the woman getting the cut.
In our day and time, gender and sexuality is being blurred, even with DOD policies buying into the social agenda known as the 'new sexual revolution' in which any and all ideas of sexuality and gender are being given a green light. Therefore it would not be surprising for appearance standards succumb to the politically correct pressure to accommodate every perceived identity in an effort to avoid offending a protected microscopic minority that is not even represented among our ranks.