The way it was explained to me was that Clarksville was a big transit point for soldiers on their way to the West Coast for transit to Vietnam. That may not be right, but it does make a lot of sense when compared to the words of the song: "... and I don't know if I'm ever coming home."
Verrrrrrrry interesting.
Since Clarksville TN which was a huge railhead from Civil War days is just south of Fort Campbell KY, major training base and home of the 101st Airborne Division which went to Vietnam in fall 1965, that would make sense.
When I shipped to RVN in 1971, troop movement was mostly by World Airways aka FarFarEastern Airlines (”Fly to exotic foreign locations. Meet interesting local people. And kill them.”)