Leper's character provides conflict because he is the character that reveals the true face of war-both literal war, and the internal war that Gene waged against Finny. In the novel, the boys don't have a good idea what real war is like; they just romanticize the soldiers in uniform that are going off to bravely defend their country. Well, Leper represents the other side of that, the more ugly face of war. After he leaves training camp, he is highly disturbed; the pressure really got to him. This is what war often does to people, but most of the boys don't realize this. When Gene goes to visit Leper in chapter 10, Leper describes how because of the stress, lack of sleep, and fear of fighting, that he started hallucinating, seeing things, and doubting his sanity, so he was released. He says, "And the perfect words for me...psycho. I guess I am." This presents Gene-and the other boys-with a more realistic viewpoint of war, and it adds tension and conflict to the storyline.
Leper is also the one who brings the ugly side of Gene's war with Finny to the light. In the auditorium, it is Leper who finally reveals the truth of what happened that day at the tree. In chapter 11 he describes,
"The one holding on to the trunk sank for a second, up and down like a piston, and then the other one sank and fell,"
which finally unveils Gene and what he did to Finny that day. Gene had, in a way, waged a war against Finny in his mind. Because of Leper's description, Finny finally accepts what had happened, and flees, to his fate. So, Leper brings to light the truth of Gene's personal war with Finny, as well as real war, and that provides much of the conflict of the story.
Brinker is the popular guy that everyone loves, except for Leper, because Brinker always picks on Leper. So that dynamic provides conflict in and of itself. Brinker is also the one who sets up the "investigation" of Finny's accident. He says to Gene: "Tonight we're investigating you." So, he prompts the crucial point that leads to Finny's fall.
These two characters, though not the main ones, are crucial in moving the plot forward, presenting necessary background information, and adding dimension and depth to the storyline. I hope these ideas helped. Good luck!