In my RP characters I usually come at constructing them from the approach of pinning one or two traits together that I want to study and experiment with (i.e. Hubris and Wisdom in the case of Ishi.)
I tend to take a DND/literary/longest possible list of questions approach to constructing characters, as well as sitting down and spending far too much time letting them roam around in the world of words outside the RPG. Before I plop a character down into the game I always try to know some mannerisms, speech patterns, etc. of that character. Are they racist or welcoming of all cultures? Are they proud and ignorant, or shy but brilliant? Do they enjoy contact with others or time alone? After I answer some of those questions, and a whole lot more, I begin kindly jamming their little minds with things I want them to say and see if it feels right or not. In the case of Ishi Polzin, I have absolutely nothing in common with the character save a love of learning. As for Koga, he's just one of those typical power hungry elites, with far less compassion for people than I have personally.
I guess what I'm getting at is I always try to give a character time to develop into something other than myself, or a facet of myself, before I toss them into play. Naturally, some personality traits or quirks (such as Ishi constantly flipping a coin or rolling a die), come through from my real life, those little meta moments. Adding our personal life experience helps a constructed character feel a little more, well, real, in my opinion.