Although the marriage gives her name as Eliza Jane the 1871 census gives her as Jane born Patrick abt 1832. The children by James in the IGI also gives her as Jane Gawne. In 1871 they are living adjacent to her parents , Thomas Gawne and Jane Sayle. I cannot find an entry for a James and Jane Gawne marriage but we cannot rule out the possibility that it was separate from the James and Eliza Jane marriage. Furthermore, in 1871 there is a daughter Jane aged 18 who would thus have been born about 1853 but no record for her is in the IGI so whether she was James' daughter or Jane's or James and Jane's is moot.
Perhaps someone can look up James in 1851/61.

1871
Summer's Lane, Peel
Eleanor M Gregory 4 Peel, Isle of Man, Isle of Man Daughter [Peel] Isle of Man
Emily I Gregory 9 months Peel, Isle of Man, Isle of Man Daughter [Peel] Isle of Man
James Gregory 36 Peel, Isle of Man, Isle of Man Head [Peel] Isle of Man
James Gregory 6 Peel, Isle of Man, Isle of Man Son [Peel] Isle of Man
Jane Gregory 39 Patrick, Isle of Man, Isle of Man Wife [Peel] Isle of Man
Jane Gregory 18 Patrick, Isle of Man, Isle of Man Daughter [Peel] Isle of Man

1881
10 Queen St, German - Peel, Isle of Man
James GREGGOR Head M Male 46 Peel, Isle of Man, England Fisherman
Jane GREGGOR Wife M Female 49 Malew, Isle of Man, England
James GREGGOR Son U Male 17 Peel, Isle of Man, England Fisherman
Emily J. GREGGOR Daur Female 10 Peel, Isle of Man, England Scholar
Alice GREGGOR Daur Female 6 Peel, Isle of Man, England Scholar

1891
Gryger, Alice 16 Peel, Isle of Man Daughter German Isle of Man
Gryger, Annie 49 German, Isle of Man Wife German Isle of Man
Gryger, James 56 Peel, Isle of Man Head German Isle of Man

Burials
GREGGOR, James 61 Ger 4 May 1895
GREGGOR, Jane 54 Ger 4 Jul 1888 ?? age not exact?
GAWNE, Eliza Jane 20 Bal 24 Jan 1865

Jane