As a kid I sang this as part of a voice recital, and it was a fun song then! For some reason, I recall there were also little asides after each of the verses... might have come from a music hall rendition, and I am sure I didn’t “get” the references, but pretty sure they were there somewhere. Here’s what I recall from memory... the first four lines were an “a” part similar to the chorus, the second four lines were a “b” part starting on the IV chord.

I am Captain Jinks of the Horse Marines
I often live beyond my means
I sport young ladies in their teens
To cut a swell in the army
I teach young ladies how to dance
How to dance, how to dance
I teach young ladies how to dance
For I’m their pet in the army

I... am... Captain Jinks of the Horse Marines
I give my horse good corn and beans
Of course ’tis quite beyond my means
Though a Captain in the army

I joined my corps when twenty-one
Of course, I thought it capital fun
When the enemy came, then off I run
I wasn’t cut out for the army
When I left home, Mamma she cried
Mamma she cried, Mamma she cried
When I left home, Mammy she cried
“He ain’t cut out for the army.”

The first day I went out to drill
The bugle-sound made me quite ill
At the balance-step, my hat it fell
And that won’t do for the army
The officers they all did shout
They all cried out, they all did shout
The officers they all did shout
“Oh! that’s the cure for the army.”