I've been listening to this since I was 19. I'm 65 now and I still wonder about this lyric. Jim's version is the one I've been following for a long time now. All I can add is this:

I'll be down there in the last bread wagon.
I'll be there with my head in my hand.
When the boys goes to no man's land,
I'll be there, but I won't be fighting.
I'll be there dodgin shotgun shells.
I won't be fighting, but I'll be runnin' like hell.
When the boys goes over the top out,
And they're kickin' down the eagle rock,
I'm gonna beat 'em to the dugout and dodge those shotgun shells.

Y'all probably already know this but "Eagle Rock" was a popular 1920's black dance performed with the arms outstretched and the body rocking from side to side. "Doing the eagle rock" is also a metaphor for sex. Leadbelly did a piano solo called Eagle Rock and mentions the term in a number of other songs. In his intro to this song Leadbelly says "this is a song they did in 1917, the boys all got their bonus" and goes on to tell how the boys "didn't have a nickel the next day," because the girls just "smacked the money." So I assume this is a tongue in cheek lyric having to do with men somehow associated with WWI and the ladies of the evening that followed them around.