William is possibly your link - there were no Gellings in my 1796 Gore's directory (I looked it up last night!) which lists most tradesmen etc - Liverpool saw major growth from 1770's onward and dragged in many Manx.

The Mansfield is explained but I couldnt find any ref to a Mansfield family on the Island - thus it is likely that William came over unmarried - catch is the late 18th/early 19th period is difficult to bridge - try looking for all William G's born on Island within timescale but you need access to burial records etc to remove suspects - use of the Manx Museum Wills index might help but not that practical from NZ though you can research wills via Mormon films - see my site under genealogy etc.

Betsy is short for Elizabeth (ie ElizaBETh -> BETty or BETsie - the ty or sie sound being a common feminine diminutive which shows endearment (or at least that's the theory I read on the pyschology of names - apply the same suffixes to a male and you may be insulting him!)
(my pages are http://www.ee.surrey.ac.uk/Contrib/manx/index.htm)