Beg, you are doing a great job there on the NZ board trying to help out Russ

I will make any comments here on the Scottish Caithness board and leave you to follow through on the NZ board as you think best.
What were the names of the children of Andrew and Mary, in order and including any middle names used (particularly useful if they were surnames as middle names!). Wondering whether Mary may have used any form of naming pattern for the names of her children (many sites/links on this, one here that I like
www.halmyre.abel.co.uk/Family/naming.htm). I can see the first born son Henry in 1864 from what has been posted?
The main key info I have now seen for Mary is that her birth place was in the Parish of Thurso in Caithness (this map here shows you parishes for Caithness).
The Mary we were looking at earlier was born in Latheron, some distance away.
The Mary you found earlier and mention in the other post would have fitted very well (daughter of Donald)....except the family show in Canada by 1851 (supported by the remarks on their 1841 freecen entry:
I have found a new Mary, showing as Maria in 1851 which might fit (Ancestry have made a mess of this transcription, this is from freecen):
John Gunn 60, (Pauper) Organ Player, b. Paris
Elizbeth Welch Gunn 50, b. Liverpool England
William Gunn 19, fisher b. Thurso
Jane Gunn 18 b. Stromness, Orkney
Elizbeth Gunn 17 b. Thurso
Maria Gunn 12 b. ThursoAnn Gunn 9 b. Thurso
Rose Gunn 6 b. Thurso
Address: East Side Of Church Yd, Thurso
For 1841, Maria is showing as Mona:
John Gunn 42, ship's carpenter b. Foreign parts
Betsey Gunn 34 b. England
John Gunn 18
William Gunn 15
Jane Gunn 13
Betsey Gunn 7
Mona Gunn 3
Address: Thurso Shore Street
As before, will be a case of getting additonal info to include or exclude this family and Maria/Mona. The names of Mary and Andrew's children may help for this (hopefully!).
Monica