From my research I found that Joseph Carroll Sheehan was enlisted in the U.S.Army during the period of June of 1916 thru Sept of 1920
As fate would have it he was inducted at Jefferson Barracks, Missouri - as an aside, his Mother and his Aunt Bridget died in the state of Missouri -
When separated from Service he held the rank Sgt. and had been assigned to:
Co "A" 8th Engrs Co "A" 1st Bn Mounted Engrs
At the time of my several inquiries to the military archives the only records were of this particular service with no mention of serving in the US Navy.
Also, at the time of his enlistment he had been divorced from Josephine for a couple of years.
Not too long before her passing, Mom told me about her meeting Joe Sheehan prior to her marriage to Dad. She said that he as a good looking man with light hair and perhaps not in the best of health.
As for Aunt Eleanor's supposing that Josephine received a government pension based on Joseph's military service does not ring true - however, remember my last blog post mentioning that Josephine was listed a nearest relative on Peter Brennan's WWI Draft Registration Card, in my opinion it would be more likely that any military widower government pension would have been based on Brennan's service.
The Military Archives would be the place to inquire as to Peter Brennan's military records - these records may include an application for widow's pension with an affidavit from Josephine.