An interesting little item came up on eBay...associated with a now-defunct military academy:

s-l1600.jpg

The case also has a monogram, so I'll assume it was presented to a graduate (May being a typical month for graduation).

As mentioned above, the academy is defunct:
Gulf Coast Military Academy Was founded in 1912 by Col. James Chappel Hardy in Gulfport, Mississippi and was a West Point Honors Military Academy. The Senior Branch of the Academy was closed in 1953. and the grounds were purchased by the federal government.

Apparently the site is a retirement home for Armed Forces personnel today.

The watch is a nice little Hamilton fixer-upper in a factory case:
https://www.ebay.com/itm/184165602891?ul_noapp=true