So I was casually doing a Veronica Mars rewatch for no particular reason (lol) and found a possible canon basis for Logan joining the military. In 1.13 Lord of the Bling, the episode after his mother disappears, Logan explains to Duncan why he believes his mother is still alive.
"You know mom’s dad fought in the Korean War? Well he got this lighter in Seoul. He held onto it even when he was captured. He and his buddies escaped and he had it engraved.
"It was always in her purse but she left it on her dresser the night she disappeared. It’s a sign.
"She hated all this…They didn’t find a body because she’s not dead, she just escaped.”