Re: Elizabeth Braithwaite update
Having (finally) got my hands on the Kendal parish registers I can confirm that William the watchmaker is indeed the one who married Mary Allan on 31st August 1812 at Kendal Holy Trinity: the clincher is his description as watchmaker for the baptisms of the 2 eldest children (NB Miles his eldest son died in infancy - which accounts for his youngest son being christened Myles). Mary was the illegitimate child (born 7th April 1796) of Jane Allan and was only 16 when she married William - which was "with permission of guardians" (suggesting Jane had died by then?).
As to who William was: no really conclusive proof. I did try to prove that the William born in Kendal in 1782 died as a child but I gave up because of lack of time. That leaves the son of Joseph & Isabel (née Johnson) of Casterton baptised at Kirkby Lonsdale on 6th May 1781. I have more details if required.