Back on track after my William BROWN confusion - I pick up with proving George BROWN and James BROWN are brothers. Thereby proving that the William BROWN on the 1891 census is indeed related to me.
I had previously sought to prove George BROWN and James were brothers and so had some of George's records at hand. George's death record states that his parents are John BROWN and Jane [Jean] Maxwell:
Statutory Death Record of George BROWN - 1862
James BROWN's death record also gives his parents as John BROWN and Jean Maxwell:
Statutory Death Record of James BROWN - 1873
This proves that James and George are brothers. A search for BROWN births in Glencairn show that there was also a William born to John BROWN and Jean MAXWELL:
Birth Record of William BROWN in Glencairn Parish Register - 1807
So, I have proved the heads of household at Woodhead, George and James BROWN are brothers. I have also found the existence of another brother, William (as there are no statutory death records of a William BROWN with a mother named MAXWELL, I can only assume he died before 1855).
I have therefore come to the conclusion that the William BROWN (b.1829) living at Woodhead on the 1891 census is in fact James BROWN's nephew.