Thanks for the updates.
I still have not found the source of Billy's song.

However, to correct a couple of things:
Billy Barker is now known not to have been a Cornishman or "sailor" per se. He was from the March area and was a canalboatman.

The Klondike (Klondyke) goldrush was in the Yukon in the 1890s and not connected to the Cariboo or Fraser River rushes from 1858 to the 1860s.

I agree with Bob that the song could well be a snippet of a music hall song as those are the songs that were presented at the Theatre Royal in Barkerville, where I am now the producer.

Thanks for everyones ideas

Richard