Absent some battlefield heroism, what is the usual point of a squire becoming a knight? Is it just the nebulous opinion of the knight he serves, or was there a certain checkpoint like a term of service or a particular age where he got knighted, so long as he had progressed to the satisfaction of his sponsor? Or was there an achievement, like serving in battle without disgrace (Prince Aerys) or winning a formal joust or tourney (Harry Hardyng)?

I mean, age, achievement, the knight’s opinion, all of these things played a role. However, there’s one factor that you didn’t mention which was quite significant in determining if and when a squire became a knight: money. 

See, a knight was expected to pay for their own arms, armor, horse, etc. and not every squire could afford to do that. So there were quite a few examples of fully-trained, fully-grown, battle-tested men-at-arms who might spend their entire military careers as squires.