There are several scenes in the book between Brinker and Gene that may be considered to be relevant and significant. The first one that I can think of is shortly after Finny's accident Gene goes downstairs with Brinker and is around the other guys smoking. He is very nervous as Brinker keeps making innuendos about the accident. Gene deals with it by joking in agreement.
Later in the story Brinker feels compelled to make Finny face the truth about his best friend and confronts Gene in front of Finny. The truth coming out results in Finny trying to get down the stairs too quickly and falling which ultimately leads to his death.