It certainly shows the connection with John's occupation before he left England. Averil just posted this:
"1861 Census R.G. 9/2724
Liverpool

Stanley Street North

William Corkill Head Mar 45 Stone Mason Isle of Man
Jane Corkill Wife Mar 43 Isle of Man
John Corkill Son Unmar 22 Stone Mason Isle of Man
Robert Corkill Son Unmar 15 Plasterer Isle of Man
Ann Jane Corkill Dau Unmar 12 Isle of Man

John Corkill not with the family in 1871"

So this all fits with what you had been told about when he went to NZ, and gives his previous occupation.
There were a lot of Corkill blacksmiths and farmers in the IOM, and if we could find them in 1841 it could be a big help - occupations were given in that census.

In my last message I wrote what I could find about the possible parents Thomas Corkill and Elinor Callow.

Patrick Corkill and Catharine Creech are much easier to find, but William isn't with them. Note son James's occupation.
1841 Maughold census:
2 23 122
Pt of Ballagilley
Patrick CORKILL 69 Farmer Isle of Man [he died in 1843]
Catharine CORKILL 49 Isle of Man [in 1851 she was in Curragh Dhoo Maughold, farm prop, 17 acres]
James CORKILL 19 Isle of Man
Esther CORKILL 16 Isle of Man [in 1881 was housekeeper for brother James, wid, stone quarrier]
Jane CORKILL 14 Isle of Man
Margaret MOORE 27 Isle of Man [eldest daur - marr.John Moore 1839]
John MOORE 21 Ag lab Isle of Man
Robert MOORE 2 Isle of Man
William LAWSON 2 Isle of Man [bapt 1839, illeg son of Wm Lawson & Cath Corkill - daur Cath b.1817]
John MOORE 2 days Isle of Man

Sue