Like most of the characters in the novel, Leper and Brinker hold significance largely in their relationship to Gene. These two characters teach Gene different lessons and challenge him in different ways.
Brinker is one of the three central characters in the novel. Along with Finny and Gene, he is part of a triangular character unit. Brinker and Finny represent the two paths that Gene feels he can follow. Brinker is responsible. He also (as in the example of the trial) expect others to take responsibility for their actions. Of the boys still at Devon, Brinker is the most grown up.
This set of traits is in direct contrast to Gene's other major influence, Finny. Finny is childish and irresponsible. Much of Gene's conflict in the novel comes in his struggle to choose who to adopt as a role model, Brinker or Finny.
Leper does not fit into this triangle. Leper does not have the kind of symbolic or representative nature that the characters of Finny and Brinker do. Leper's primary role, ultimately, is to help Gene see himself clearly. Instead of functioning as a role model like Finny and Brinker, Leper functions more like an oracle.
When Gene visits Leper in Vermont, Leper reveals the fact the he knows Gene knocked Finny from the tree. Leper resists Gene's evasiveness and tells the truth.
Leper, aware of Gene's contempt for him, strikes back, calling him "a savage underneath."
Where Finny and Brinker both present "ways of being" to Gene, also offering advice at times, Leper presents only a point of view.