Guess what. Bob Dylan ALSO has a song with the title 'When The Sun Goes Down.'

In the evening, baby, when the sun goes down
    In the evening, when the sun goes down
          Sure gets lonesome when your baby's not around.

   
Sure gets lonesome, sleepin' all by yourself
Sure gets lonesome, baby, sleepin' all by yourself   
    When you're lovin' somebody, and she's sleepin' with somebody else when the sun goes down

In the evening, mama, when the sun goes down (Oooh Lord)
   In the evening, when the sun goes down
         Sure gets lonesome when your baby's not around,
             when the sun goes down.

In the evening, in the evening, mama, when the sun goes down
In the evening, mama, when the sun goes down
Sure gets lonesome when your baby's not around,
when the sun goes down.

So this just muddles the pot because it's obviously based on the song Leadbelly, Robert Lockwood Jr and all those other artists, but I have not been able to find a single song-writing credit for the Dylan version.

Musically, there's not really any similarity other than that it's a standard blues. It's the first track on a Dylan album I found called Back Pages.