We might describe the characters of Brinker, Finny and Gene as being parallel to the classic Freudian theory of the Id, the Ego and the Super-Ego.
Finny is most like the Id, driven by impulse, defined by his spirit. He is a figure of inspiration, capable of getting away with almost anything because, in part, he feels little guilt in following his whims. These qualities match the free-wheeling summer session where the rules were loosely enforced and self-exploration was a central concern.
Brinker is most like the Super-Ego, defined by his conscious choices. He is fully socialized and has an air of sophistication. He not only follows the rules, Brinker also helps to enforce those rules and even create some via the committees he heads. Brinker's character is expressive of the winter school session, where the rules were brought back in full force and preparation for the impending future.
Gene then is most like the Ego, navigating and monitoring the impulses from these opposite directions, choosing which to hear, which to heed, and which side best defines him.