Well, after he left Brokeback in 1963, he still lived with his parents. He went home to them and hung the shirts in the closet. But that is not the only reason they remained there. He kept them there to keep them safe. His parents' home was the fixed place in his life that stayed the same, where he could go back to time and again, go up to his room, look out that window and dream as he did when was a boy. Everything in his room remained the same...therefore he put the shirts there because his room was the most sacred of places for him. There he kept the one thing that was most important in his life. He kept that love for Ennis safe and in a place where no one could ever take it away or harm it. The shirts are also symbolic because they hang in a closet. Symbolic of Ennis and Jack's relationship which was kept a secret. After Jack passed away, and Ennis went there, he took the shirts out of the closet...he carried them downstairs with him in full view of Jack's parents. For the first time in his life, he didn't care if anyone knew. He was finally open about what he and Jack shared. He took the shirts home with him and kept them in a place that was more open than a corner of a closet...he made it into a shrine.
He finally openly acknowledge the relationship and the love. He had come a long way from his usual reaction when he felt that people suspected...look how he yells at Alma and gets angry at the Thanksgiving scene. He used to feel so threatened when someone dared mention his and Jack's secret...confrontational, defensive. In the end, he doesn't anymore...he doesn't feel he has anything to hide anymore. He finally accepted himself fully, accepted that he'd been wrong to deny Jack the life together they deserved. He realized how much he had hurt Jack, and he realized that it was the best thing that ever happened to him, and he had been wrong to treat something so beautiful as if it was a dirty little secret. I always get the feeling Jack is watching over him in the end...smiling and thinking "I knew he'd come around some day." The shirts had been Jack's way of keeping Ennis in his heart forever, and then when Ennis takes them home and puts Jack's shirt inside his own, it means he is keeping Jack in his heart, in a safe sanctuary for all of time. The center pieces of his little trailer home becomes the two shirts...the memory in his heart of the best, most wonderful thing in an otherwise lonely, difficult, sad life, his true love with Jack.