Jimmy is the youngest Todd, and the one we know the least about. His only defining moment occurs when he joins the war because he wants to be a writer, and "what better than a war to reveal to him the heights and depths of the human condition?" (21.233). In this way, he mimics his father, Hugh, who left for war to have an adventure.
Later, it's also revealed that Jimmy is gay, almost as an aside by Ursula and Pamela. So, good for Jimmy, but why should we care? We're given very little incentive to care about him ever, and we're not about to start now. Cold, we know.