The verse that is a part of the 'prisoner' songs belongs to an English song that became popular in America near the beginning of the 19th c, printed in sheet music and arranged in America for duet in 1812.
"Meet Me By Moonlight" a song for lovers meeting by moonlight, has persisted as a floater in other songs. The original song, by J. Augustine Wade, London, undated in Levy, was arranged for duet in an 1812 copy printed in Philadelphia and composed by Mrs. Seguin and Mr. Shrival.

MEET ME BY MOONLIGHT
(Mr. J.Augustine Wade)

Meet me by moonlight alone
And then I will tell you a tale.
Must be told by the moonlight alone
In the grove at the end of the vale.
You must promise to come, for I said
I would show the night flowers their Queen
Nay turn not away that sweet head-
'Tis the loveliest ever was seen.

Oh! meet me by moonlight alone
Meet me by moonlight alone.

Daylight may do for the gay-
The thoughtless, the heartless, the free-
But there's something about the moon's ray
That is sweeter to you and to me-
Oh! remember, be sure to be there,
For tho' dearly a moonlight I prize,
I care not for all in the air,
If I want the sweet light of your eyes.

So meet me by moonlight alone,
Met me by moonlight alone.

Not in the original song, but added to the duet-
Yes, I'll meet thee, I'll meet thee by moonlight alone.

The Wade original, printed by F. T. Latour, London, is here: http://levysheetmusic.mse.jhu.edu/cgi-bin/display.pl?record=115.006.000&pages=6