Bob, well besides the Oxley information which I will provide below (Eliza Jane Gill married into the Oxley family) I am not sure I have much more that can help!
John Holbay Oxley was born April 01, 1844. His parents were John Oxley born in Nottinghamshire in 1806 and Cecilia (Cicely) Holbay born in Sheffield in 1811. They had the following children:
Selina born 1849 Mary Ann born 1836 William born 1841 Harriet born 1838 George born 1833 John Hobrey Fanny born 1845 (Married Robert Stocker).
Maybe the connection is through marriage to one of the GILL or OXLEYs and I dont know their spouses yet?
I just cant say I'm sure, it has to be somewhere immediately around Eliza Jane, if this is true, since she had so many male relatives around her, I'm not sure how such a statement could be made. Fo rinstance, it was her brother who mentioned if she were male she would have inherited it. Maybe it was something like she was a good friend of your family and if she were a male they would have gifted it to her? But why would he have said "inherited" then! This will perhaps be a forever mystery! Do you have a GEDCOM of your family somewhere? I could look through it and see if anything rings a bell on my side!