In 1892 he was appointed by Li Hongzhang as examiner of naval engineering graduates at Imperial Tientsin University, China.

During the Spanish–American War he was chief engineer on the USS Amphitrite, which participated in the bombardment of San Juan.

During World War I, Eaton was recalled to service as Inspector of Engineering Material and Ordnance in Cincinnati.

[4] Eaton was a freemason and a shriner and was one of the founders of the Mystic Order of Veiled Prophets of the Enchanted Realm, an appendant body of Freemasonry.

Eaton was "one of the pioneers of Lincoln Cent collecting, and perhaps the only person to take this activity seriously within the numismatic community at the time".