(My reply to a theory on Reddit)
It’s hard to measure age when you time travel, really. If you always travel from midday to midnight, and you count your days, do you divide by 2?
Or do you keep a watch that counts your seconds, then divides them to form Earth years?
Do you measure how much the body ages? Well, human bodies don’t age at precisely the same rate, Time Lords’ doubly so.
Age is a human construct that assumes that nothing timey wimey happens.
I do like to think that the TARDIS keeps count, though. Although in the case of 11 and Trenzalore, they hadn’t seen each other in decades.
I also speculate that for someone like the Doctor, age doesn’t matter, but they amuse themselves with the way it does for others. Maybe like other human constructs like marriage (the 1st Doctor’s “I made some cocoa and got engaged” or the 11th getting married for a green card into the Teselecta) – he flouts these constructs that grow thin and irrelevant when you’ve lived that long and travelled through time that much.
That being said, that is a theory and yours is a theory and both are perfectly fine 🙂 Thank you for inspiring this answer.
As far as the meta goes, I doubt that any of the writers had any answer in mind.