One way of trying to find Alexander Arnotts death (or at least to narrow it down) is to look at the marriage records of his children,
We know when his son David Arnott married in 1870, his father was deceased.
His son John Arnott; married Margaret McGregor in 1864 Blythswood. What does the record give about his father?
His youngest son Alexander married in 1855 Does this marriage record say his father was alive or dead?
We know he was alive in the 1851 census.
Here is some information about his youngest son: -
Alexander Arnott (junior) married Catherine Austin in 1855 Calton Glasgow
Children:-
Prudentia - born 1855 Glasgow
Catherine - born 1856 died 1857 Glasgow
Alexander - born 1857 Glasgow
Elizabeth - born 1860 St Giles
John W - born 16 Jan 1862 Farnham / Aldershot, England
David born 20 Dec 1863 Dover, England
Mary Ann - born 1867 Gibraltar
James - born 1870 New Brunswick, Canada
1861 census Alexander is with his family in Greenlaw / Glencorse Barracks, Midlothian (part of a detachment of 78th Regiment of Foot / Highlanders )
The regiment embarked for Gibraltar in 1865, and then in May 1869 sailed on the HMS Crocodile troopship to Nova Scotia, arriving on 14 May 1869.
Private Alexander Arnott was discharged from the 78th regiment in April 1871 (There are service / pension records for him on Ancestry Fold 3)
1871 census in New Brunswick Canada. Alexander (36) is a Tobacco Pipe Make.
Wife and all his children with him.
In late 1871 / early 1872 the family moved to Boston Massachusetts. Many of his children were married there.