Jon,
As I wrote earlier 'Tomlinson' is a very common surname so Tomlin and similar spellings must have been at one time a very common Christian name. (Mary Poppins--David Tomlinson was the father.

The capitalisation and lack thereof is a common indicator of age in street lit. Up to about 1780 it was very common to capitalise most nouns, but not consistently so, even in the 17th century, so the later non-capitalisation is another indication of their differences in age. Obviously this is not a hard and fast rule and some capitalisation carried on into the 19th century in outlying places.
I would still like to see a copy of the c1765 garland again. It's possible I have it on an ECCO disc somewhere but finding it would take me ages. Do you have the actual references to the 2 copies? So that I can compare with my references.

Yes, once we get into the late 18th century northern England/Scotland is where it turns up and then back to England in the 19thc printings.
All we can say regarding likely origins is that the song was known in London and Scotland in the 16th century.