I do not know when he joined the Navy, but I have no record of a draft card so it would seem that he enlisted. He was assigned to serve in the Southwest Pacific Theater on the USS Canopus (AS-9) as a warrant officer. The ship was a submarine tender. The Canopus was scuttled after the surrender of Bataan, and her crew were evacuated to Corregidor, where they served in the Marines 1st, 2nd, 3rd, and 4th battalions. Most of the crew were captured at the fall of Corregidor on May 6, 1942, including Eugene Arthur Gammon. He was taken as a POW by the Japanese military and apparently held captive for two years.
The Japanese used unmarked freight ships to transport their POWs in horrible conditions, earning them the name "hell ships." These ships were often attacked by American forces who were unaware that they carried American soldiers. One such ship was Arisan Maru, which was hit by three torpedoes from an American submarine, either the USS Shark or the USS Snook, on October 24, 1944. It was carrying almost 1800 prisoners from Manila to Japan, including Eugene. Only nine prisoners survived the sinking of the Arisan Maru. Eugene Arthur Gammon was lost when the ship sank in the South China Sea. His name is among the tablets of the missing at Manila American Cemetery in the Philippines.
He has two gravestones in America. One is in Fort Logan National Cemetery in Denver, Colorado. He is also included on his parents' gravestone at Evergreen Cemetery in Colorado Springs. Here's a photo of the stone in Denver:
Eugene was awarded the Bronze Star, Purple Heart, and Prisoner of War medals, presumably posthumously.