Hmm . . . a cousin (some years older than me) was drafted during the tail end of the Vietnam war. He went in, served honorably, and was LUCKY to be stationed in W. Germany. As he told me later, just a few days before his discharge he was presented with paperwork to sign up with the Reserves. He was told he HAD to sign up as part of his "obligation."
He flatly refused. They gave him a lot of grief over it, but he dug in his heels and wouldn't sign - two years active duty was enough for him. A lot of other draftees he knew whose enlistments were up refused, too, though some signed up. Apparently a lot weren't even told/asked to sign Reserve papers, so whatever "policy" was being applied wasn't being applied uniformly across the board.
He got his Honorable Discharge as scheduled, and it came with a tongue lashing from some officer. No Reserve sign up.
This was right around the time both the Vietnam war and the draft ended, so I guess there was a lot of stuff going on with enlistments and recruiting that didn't make the papers.