Since he had Military Honors the Funeral Home should have his DD214 details or at least a copy of his Honorable Discharge Certificate. Also the Cemetery may have some details. Since he was born 1946 it was probably service in the Vietnam War.
I hope you have the correct death date as what you have posted is incorrect. Also middle name could be spelled Eugene in records even if it is Eugine as people and transcribers will sometimes "correct" a spelling whether needed or not. I have an relative that her birth record has the name first name as Lori but her death record it is Laura.