The John in the 1871 census entry which Liz found is in the IGI (extracted entry from the par.reg). The register entry would almost certainly read: John James illegitimate son of Elizabeth GAWNE bapt 23 Feb.1864 Lonan. Even though he is put in the IGI under surname Gawne, the entries themselves didn't usually read like that. And in the usual Manx way he would be known by the father's name, even when the father was not mentioned at baptism.
In Liz's 1871 census entry John James of the above bapt is at Agneish Lonan with grandparents Richard Gawne 61 mine labourer b.Arbory & wife Elizabeth 62 b. Arbory, unm daur Elizabeth 27 dressmaker b.Lonan, Moses Quine G.Son 9 b.Lonan, John Mylchreest G.Son 7 b.Lonan, Annie Mylroie G.Daur 2 months.
Moses bapt 25 Jan.1862 Laxey son of Ann Gawne.
Ann bapt 9 Jan.1837 Arbory daur of Richard Gawne & Eliz Radcliffe?
Elizabeth bapt 6 Feb.1842 Patrick daur of Richard Gawne & Eliz Radcliffe?
Sue