James, I served (MOS 2402) in the US Army for three years between 1962-1964, overlapping into your Viet Nam War Veteran yearly range by one year (1964). My service was stateside (ASAHQ, NSA) and overseas (Germany, Frankfurt). I would never and could not in all good conscience describe myself as a Viet Nam War Veteran, even though I served in 1964. I believe the proper "era" within which to describe my service is not the Viet Nam era, but the Cold War Era as described below:

Cold War Recognition Certificate
In accordance with section 1084 of the Fiscal Year 1998 National Defense Authorization Act, the Secretary of Defense approved awarding Cold War Recognition Certificates to all members of the armed forces and qualified federal government civilian personnel who faithfully served the United States during the Cold War era, from Sept. 2, 1945, to Dec. 26, 1991.

Who is eligible? All members of the armed forces and federal government civilian personnel who faithfully served the United States during the Cold War era, Sept. 2, 1945, to Dec. 26, 1991.

The Cold War Era includes the Korean War, the Viet Nam War, The Cuban Missile Crisis and a couple of others I cannot recall. Unless I am wrong, DOD has not formalized any period of time, or Certificate of Recognition specifically for the Viet Nam War. If you know otherwise, please do let me know.