Agreeing with this.

There are societies that label all gay people a "third gender", but then differentiate between the gender conforming & cross-gender conforming ones.

Most "third genders" in cultures I know are always very strongly patriarchic societies, and third gender are always gay, weak or infertile men who have less rights or power than men, but more than women. In most cases it is something like "to not shame males with you being not manly enough - we will say you aren't really a man". Women never got such "thrid gender" group (except few islamic countries, but there it is different, I'll explain later). Mostly women were pretending to be men in cases when women wanted to be free from oppression, or to learn science or to work on some jobs (like surgeon) which were forbidden for women to work. Other case is when lesbians were trying to live together, and only way was if they moved to new place and one was pretending to be a man on public ("Sea Purple" nice movie with this part, thought it was forced there). In those Islamic countries I've mentioned before - when husband of woman died, and she has no sons, no brother and no father alive, then she can inherit what her husband owned, but she must try look masculine, wear masculine clothing and never marry or date men ever again.