How does the Master turn into a woman? How does a sex change work in Time Lord regeneration?
In the episode The Doctor's Wife, we get this line:
DOCTOR: The mark of the Corsair. Fantastic bloke. He had that snake as a tattoo in every regeneration. Didn't feel like himself unless he had the tattoo. Or herself, a couple of times. Ooo, she was a bad girl.
Additionally, in the short The Night of The Doctor, we get this:
OHILA: Mock us if you will, but our elixir can trigger your regeneration, bring you back. Time Lord science is elevated here on Karn. The change doesn't have to be random. Fat or thin, young or old, man or woman?
Based on these pieces of dialogue, it is safe to say that changing sex after regenerating is normal, if rare, and the Master's regeneration wasn't unusual in this regard.
Some Time Lords, such as Romana in Destiny of the Daleks, are shown to have more control over their regenerations than the Doctor does.
In particular reference to The Master, when he regenerates from his Professor Yana incarnation to the Harold Saxon version he deliberately chooses to make himself younger.
YANA: Killed by an insect. A girl. How inappropriate. Still, if the Doctor can be young and strong, then so can I. The Master reborn.
The only sources I'm aware of that explicitly dealing with how a Time Lord might regenerate into a member of the opposite sex are the non-canonical:
- Exile in which suicide triggers a "sex-change regeneration"
- The Curse of Fatal Death in which the Doctor uses up all his regenerations, but is granted another one by the universe and comes back as a woman.
I recall a novelisation (I can't remember the source for that though) mentioning that most Time Lords keep roughly the same appearance throughout all their lives and generally appear slightly older with each regeneration. It calls out the Doctor's dramatically changing appearance as a consequence of his lifestyle. The inference here is that the more chaotic the death, the more a Time Lord's appearance will change. This suggests that a sex-change regeneration could be triggered by an exceptionally unexpected death.
Possibly state of mind plays a factor (calling back to Exile's theory). The John Simm's master was more than usually unhinged and died after starting a fight with a mythical figure.
ALTERNATE THEORY: Recall 'The Keeper of Traaken'? At the end of that, the Master doesn't regenerate; he gets a new body by possessing Tremas. This happens again in the Doctor Who movie - some 'motile dust' from the Master's urn escapes the Tardis and possesses a man. Presumably, he could do it again, only this time by possessing a woman.
Evidence in favor: Recall that after the Master died, there is a scene in which the hand of a woman - Saxon's wife? - reaches for and takes the Master's ring. If the ring is a vessel for the essence of the Master after death, then I think that by putting it on the woman would become possessed by - hence become - the Master [I also believe the scene subtly hints that the woman knew this would happen and intended for it to happen].
Who's to say the Gallifreyans have gender the same as humans? It's rather speciest of humans to believe that their knowledge and experience with gender is the same across the known universe.
Perhaps for Gallifreyans gender is merely a physiological appearance and is completely unnecessary for and totally disconnected from their reproductive system. We've seen plenty of races depicted where anywhere from one to three beings are necessary for procreation. We've also been shown a multitude of races whose genitalia is completely foreign to humans, not to mention the many races where cross-species procreation is completely impossible.
Why attempt to ascribe human limitations to Gallifreyans?