I have never heard this by Jim and Jesse, but it definitely would fit into their repertoire. I have it by the Delmore Brothers on an old album, and also on Sand Mountain Blues, County CD 110. The songs on this CD were from their later recordings for King and were done between 1944 and 1949. A CD of their early works recorded 1933-1940 is also available, Brown's Ferry Blues, County 116. There is no mention that it is a Delmore original, but I would suspect that it is. They were close associates of Merle Travis during this period, and he is featured on this recording. Note the war reference in the second verse.

MIDNIGHT TRAIN
as recorded by Alton and Rabon Delmore, 1946

I have been all around my old home town,
I have searched everywhere I know.
I can't find any trace of my girl in this place
So there's nothing to do but go.

Chorus
I'll be riding that midnight train when it's leaving,
And I'm going away to stay.
Always wanted to know where that engine did go,
Going to go where it goes today.

Oh, she said she'd be true 'til the fighting was through,
Said she'd wait for me 'til the end.
But she's proven untrue and her sweet love is through,
So I'm catching that train again.

Chorus

When she hears this old song, she will know that she's wrong,
Cause I'm leaving my old home town.
Oh, she told me she'd wait just to be my sweet mate,
Then she threw down my heart to the ground.

Chorus