After one or two Google searches, there are a few hints we have gathered which may point to his origin; 

He would appear to come from a family with some wealth or status who could afford to pay for this portrait to be painted, although he is painted in a thick oil impasto style which is quite uncommon for miniature portraits which would tend to be finer and on ivory or card. He somehow looks French and late 1700's perhaps judging by his wig and uniform.

The closest match that we can find for his uniform is that of The Continental Navy (the navy of the United States during the American Revolutionary War, formed in 1775. Wikipedia). It does appear to be the uniform, (blue with red facings, yellow buttons and a red waistcoat with gold lace trim) of a captain. He doesn't have shoulder epaluettes as do some of the more senior portraits of officers we have found but if this were painted before uniforms were standardized in the 1790's, this would fit in. And again, perhaps mid to late 1770's as the wearing of wigs (worn as a sign of social status) went out of fashion by the 1790's.

Our best guess is that he was a young officer in the Continental Navy in the United States during the  American revolutionary war and that this was painted on brass at the scene of the conflict or perhaps after he returned from war with a medal? It seems unlikely that we'll ever know who he was... unless someone reads this and recognises him? But the searching and piecing together of a story is so compulsively intriguing and one always learns something new.