Went back through and see the Lilliburlero connection. Seems to be connected pretty tentatively though. Anyone sing it to something that resembles 'Lilliburlero'?

The Albert Richardson tune and all the versions I've heard all use the same tune which is a variant of the ubiquitous 'Dumble Dum Deary' aka 'Richard of Taunton Dean' used by many country ditties. I also hear some resemblance to the Scots comic song 'The Lum-hat wanting a croon' (The stovepipe hat without a top).