SASEBO NAVAL BASE, Japan — A Navy corpsman from the USS Juneau stepped off an airplane and strolled into Ohio’s Dayton International Airport last December looking for a woman he never had met and whose photo he never had seen. Tiffany Gamble, in Dayton from her home in Xenia, Ohio, never had seen a photo of Seaman Blair Rezny, either. Almost instantly they locked gazes. Both knew they were looking at the right person. Without saying a word, they embraced like long-separated siblings. Rezny, 22, from Omaha, Neb., and Gamble, also 22, have more in common than their ages. In...