According to Stan Hugill, this shanty probably originated in the eighteenth century on shore. There are several variants both in England and America.
Sources differ as to whether it was a pumping shanty or a forebitter.
To ask a maid to be the bride Of a poor Jack tar. Begone, you saucy sailor boy, Begone you Jack tar. I ween, Will wed this Jack tar. She always means yes. Exactly that - fascinating reading about life at sea from Maritime History which has links to many firsthand accounts of life at sea.