13 months was the normal tour of duty for U.S. Army and USMC in Vietnam for commissioned officers and enlisted personnel. USAF rotated at different intervals because some duty stations were not in-country (i.e. Thailand, Guam etc.) Blue water USN, and carrier deployments varied but many were 7-8 month deployments.
To _Schadenfreude_: I saw more than a few field grade U.S. Army officers (O-4 and above) being relieved of command (many by General DePuy - 'The Firing General'), but they would be reassigned to some support function in-country. I never saw, nor heard of the ticket punching you're talking about. I don't doubt that here may have been a handful of O-6's who did it in the quest to make general officer, but junior officers? No way. They couldn't push them through OCS fast enough and into the field.
The very last troops left in 1975, but the start of 'Vietnamization' of the war (returning to training and joint ops w/ RVN troops) in 1971 saw the mass exodus begin. By December, 1974 most units had rotated home. Many of those sent in 1971 - 1972 did not complete a full 13 month tour because their unit rotated out.
The biggest reason for a shortened tour? For every man killed in action, another 7- 9 were wounded.