I've always kind of thought that (going to get hated on here, for this, probably) the gossip stones got this one wrong. At least a little.
I mean, have you ever played the telephone game? Things travel from mouth to ear and get lost in translation. By the time a stalfos has limped all the way back to the sacred forest meadow where that particular gossip stone is located the actual meaning of the message could have been lost. Very similar to how the triforce itself is called "Triumph Forks" by most in Wind Waker.
Since he knows so much and he helps you in your journey by enlightening you about what is to come and that which has been, it has always been my personal opinion that, instead of being the reincarnation of an ancient sage, he is, in fact, the reincarnation of an ancient wielder of the triforce of wisdom, perhaps the original.
Think about it, his role in relation to the hero of time more closely resembles that of the hero of time. The sages all need to be saved, Saria from Phantom Ganon, Darunia from Volvagia, Ruto from Morpha, Nabooru from Twinrova, and Impa from Bongo Bongo. (Also, later, Zelda from Ganondorf; though she is also the weilder of the Triforce of Wisdom, which comes in later.)
However, Kaepora Gaebora's character seems more like that which would do the saving, or at least the helping of the one who would do the saving. This is further emphasided in the game. He helps you travel more efficiently (ie flying you from death mountain/lake hylia) and Zelda (the current person the Triforce of Wisdom chooses; in this game), when escaping the castle, opens the gates so you can continue travelling. He teaches you many things, as does Zelda.
Simply put, even though he is told to be the reincarnation of a sage, he seems more likely to in fact be a reincarnation of someone connected to the Triforce of Wisdom, as his character development much more closely follows that standard.
This is all speculation and has not been backed up by any official (or non-canon, that I know of) content, but it is just how it makes the most logical sense, in my opinion.