Well, I followed a blind alley to its end. Broad arrow indicates a British military watch, Kin also known as Kintown in Okinawa is home to an American Marine base where sometimes some Royal Marines have also trained. So I searched for Phelan, Royal Marines, and found a record of John Phelan who enlisted in 1913 as a boy at the tender age of 14. Killed in action May 31, 1916, when HMS Invincible was sunk at Jutland. Still, it's a blind alley as far as this watch as the first initial is not D and this watch is newer than 1916, and what would an enlisted boy be doing with a watch this nice?, and no reason to think he might have been in Okinawa. Kudos to the British National Archives for putting service records on the web.
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