What were some examples of ways that Gene tried to identify or emulate Finny?
In my opinion, Gene was more about emulating Finny than identifying with him.
He did compare his size and appearance to Finny in chapters 1 & 2 to the degree that he noted there was only about 10 pounds difference between the two of them. He thought he had discovered like interests in sports, but after time sought to create his own identity which drove him to become a fanatic about his academics.
Like Finny with sports, Gene excelled academically. Gene sought to have a skill wherein everyone on campus would look to him about that skill. This is how they treated Finny.
Unlike Finny, Gene had a mediocre character. Although Finny valued who Gene was greatly, he didn't have the magnetic character Finny possessed. I think he was jealous of that and looked for ways to have others show interest in him.
By the middle of the novel, after Finny's leg had been broken, Gene agreed to train for the Olympics to let Finny have his moment of glory at least through someone else. I think this is an effort to emulate Finny although Gene knew he would never be as good as Finny.