The Watson family had a reputation for being stable, dependable, and, frankly, conventional to the point of boring. This wasn't to say that certain members of said family didn't have their quirks. Grandma Moira had gone a bit dotty, and Harry was an alcoholic. But John was one of the Normal Watsons. Absolutely. No question.
He did not get a wave of longing when he thought of the war. He did not miss the danger or the adrenaline or the missions. He didn't.
But when Sherlock invited him to come with him, he did forget his handkerchief in his haste.