Probably related to this Reddit post: https://www.reddit.com/r/tipofmytongue/comments/crx050/tomt_song_a_very_old_song_about_a_prostitute_that/

I know a little girl I do not know her name She hangs around the corner every night Every night She wears a watch and chain A pearly* and a cane Oh, Elsie, Elsie, Elsie** how you doing?! Goodbye my darling, I must leave you. One more kiss before I go. I'll see you Saturday night If I don't, we'll have a fight Down where the water lilies grow

* I can't recall what is actually said here. Maybe a "pearly" is slang for a pearl necklace.
** I know in the beginning of the song, the singler claims to not know the prostitute's name. Maybe this is like "pearly" and I don't actually remember what was said here.

That thread linked to The Cambrian News and Merionethshire Standard April 14th, 1871 - "Good Night Darling, sung by Miss Emma Chambers"

"Good night, darling, I must leave you,
One more kiss before I go;
I'll be here to-morrow night,
If I cannot come I'll write
Just a word or two to let my darling know"

Another commenter wrote the following:

Here's my running theory:

This is a cover of an old Alabama folk song written by one "Miss Emma Chambers":

https://youtu.be/QWgT-DCfCZ8

/u/Kurty94 found it. The lyrics are a lot sweeter and sung from the perspective of a woman (who is absolutely not a prostitute). But the chorus and the melody of the choirs match.

The document you shared show men from Alabama were also in that unit. My theory is this: they brought that song overseas and the dirty New Haven mopeens changed some of the lyrics to make it funny. I know this because I would have done the same thing

So that's my running theory so far...