Ann Jane Gawne chr 1840 is a bit of a mystery but she appears to be Ann Jane Sayle.

acc Sally McCambridge 2005: Jane Kneen married at Kielthustag a weaver called William Gawne. They took in a baby called Ann Jane Sayle [non-commital].
After 1855 widow Jane moved to Ballalough 'a dealer in eggs and a stocking-maker'. They were there in 1861. In 1865 she moved to Ballacottier near Oatlands with Ann Jane. Now known as Gawne's Cottage. At Gawne's Ann Jane had a daughter called Eliza Jane Corlett in 1865 who married William Radcliffe of Craig Cottages. After Jane's death in 1879, Ann Jane left Andreas and the cottage became derelict.

The only thing I can think of was that her mother Jane Gawne was a daughter of William Gawne, possibly illegitimate?
Ann Jane Sayle had two illegitimate children by Robert Corlett and a further two who were christened Edward Quayle and Annie Sayle.

I am not sure if this is the answer but I did consider her when looking for Brian's Ann Jane Looney. I also wondered if Ann Looney was her married name but I got nowhere with that.

Jane