I came across this thread when I was looking for any trace of this song, prompted by just having watched Rory Stewart's Borderlands. In the programme a Cumbrian sheep farmer is shown counting in the traditional way, starting with Yan Tan Tethera, which is not too far removed from run tum tattelum. The version I know has the words Eh what country folk we be.

So perhaps, it originates from Cumbria.