I am seeking the source of an old familiar tune. It was used in the 1920s for (at least) "I Don't Reckon It'll Happen Again" by Uncle Dave Macon and others:

I don't reckon it'll happen again
For months and months and months...

and also for one version of "The Old Maid and the Burglar":

About nine o'clock an old maid came in, I'm so tired, she said,
Thinkin' everything would be all right, she forgot to look under the bed...

as well as more recent songs like one strain of Woody Guthrie's "Don't You Push Me Down."

I am convinced the tune is far older, going back into the 19th century. Here is its ABC:

E E E E E E E, E E D E F

F F F F F F F F G F E D E

(like line 1)

F F F F F F F F G F E D C

It sounds like a march tune, perhaps from Spanish Civil War days or even earlier. I keep thinking I know what the precursor is, but you know how it is... I can't call it to mind. (It's not "Jingle Bells," though that's similar in some ways.)

I have a feeling it is one of those primal tunes that has been used for many, many songs.

Can anyone tell me what the original tune / song is?? And can you think of other songs that have used it since?

Thanks!   Bob