Did he enter before Jan 31, 1955? Here's a post from the VA site about war periods and benefits eligibility:
Wartime Service
Some VA benefits and medical care require wartime service. As specified in law, VA recognizes these war periods:
Mexican Border Period - May 9,1916 through April 5, 1917, for veterans who served in Mexico, on its borders, or in adjacent waters
World War I - April 6, 1917 through November 11, 1918; for veterans who served in Russia, April 6, 1917 through April 1, 1920; extended through July 1, 1921, for veterans who had at least one day of service between April 6, 1917 and November 11, 1918
World War II - December 7, 1941 through December 31, 1946
Korean Conflict - June 27, 1950 through January 31, 1955
Vietnam Era - August 5, 1964 (February 28, 1961 for NYS) through May 7, 1975. (For veterans who served in Vietnam during the period from February 28, 1961 to August 5, 1964 - this applies to certain Federal benefits only.)
Persian Gulf War - August 2, 1990 through a future date to be set by law or Presidential Proclamation.
Veterans may be eligible for certain state benefits if they served in hostile actions and received expeditionary force medals for the following:
Lebanon - June 1, 1983 through December 1, 1987
Grenada - October 23,1983 through November 21, 1983
Panama - December 20, 1989 through January 31, 1990
Other Military Service - Veterans who served during periods other than listed above, and, who were awarded an Armed Forces, Navy or Marine Expeditionary Medal, may be eligible for Real Property Tax Exemption benefits.
John E. Temple, Jr.
Co-founder of A Place for Mom