Thanks for all the ideas folks. I have followed through on them but what is missing is the latin-american syncopation. This is what makes this tune so beguiling. Stan was not slow to lift tunes from contemporary (his) hits. There is a tune that has been named the White Cockatoo (because of perceived similarity with White Cockade) but it was a popular song on the early 50s The Hop Scotch Polka.
Incidentally it was collected by Don Brian who was living in Crookwell and teaching at the High School.
The mystery tune is much later (at least in Australia) than the tunes brought to the goldfields and the ones brought by the travelling minstrel shows. For the moment it is called Stan goes Latin-American.