I agree, it could have been a little less monologue-driven. I did like The Doctor getting physically angry with The Master. It could have used more of that and less companion side stories. Any one of the companions works really well with a good writer. That hasn’t been the case a few times and Sunday was one of them. The heart-to-heart between Graham and Yaz was excellent, but ultimately lost in the busy story. When I was watching, my thought just as the scene was ending was this phrase exactly; That was a missed opportunity. They rushed through it.
Regarding the story itself; It’s possible that Brendan is The Doctor. He may have hidden his regeneration energy in that carriage clock. The Doctor can use The Chameleon Arch to store the regeneration energy while living as a human for extended periods. The Doctor’s memory is temporarily replaced with a sort of pre-loaded memory. Ruth hid hers in a fire alarm earlier this year. In Human Nature, the 10th Doctor hid his in a pocket watch. When they shock Brendan to erase his memory, he has that carriage clock with him.
If I had to guess, The Division may be what the Time Lords called the gap of time where they blocked the history of Gallifrey. It could also be the name of the branch of their government that oversaw the blocking.
If The Doctor is the timeless child, it does seem like she’s immortal. I don’t have a problem with that at all. To me, that lessens the feel of the forced & poorly handled rewrite after 11 when they realized the show would go beyond 12 actors. That may have seemed like more than enough in the 1960s when it’s safe to assume they couldn’t have imagined the show would still be on the air and going even stronger 50 years later.
Having The Doctor be the source of all regeneration, including The Master, works really well into why he hates her so much. No matter what he ever accomplishes or creates – it’s all because of her. That might just push someone to the edge of sanity. Worth keeping in mind; The Master could have been lying. Brendan may be the Timeless Child.
Personally, I’m hoping it’s her. Not to get way nerdy, but in the episode from 1976, The Brain of Morbius, the 4th Doctor sees a lot of faces of his past that had been hidden from him. That part of the current season-ender isn’t really a change. They just decided to bring it back properly and make it a major part of the story.
They show the faces of Morbius in Jodie’s flashback as she’s breaking away from the matrix. At the very least, whatever becomes of this story line – which I really like – they’ve canonized the Faces of Morbius. Personally, I’m all for this for two reasons. One, it’s been hinted at before (1976) so it’s not a rewrite. Two; The Doctor should be more than just another time lord who happens to travel around. She should be special, bigger than imagination, one of a kind, and most of all, a mystery.
I don’t want to know everything about her. I like that she’s bigger than me and my world. For me, this expansion has returned the mystery to The Doctor. It’s the same as the way Rogue One returned the mystery to The Force.