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From Wikipedia, this suggests he would have joined his regiment in Johannesburg:

The Imperial Light Horse was raised by the British in Johannesburg on 21 September 1899 for service in the Second Boer War. Its initial strength was 444 officers and men. It was informally known as the "Reformers Regiment" as many of its officers served on the Reform Committee, or more commonly the Uitlander Regiment by the Transvaal Government and the Boer Commandos.[1][2]

If her father came from a family of soldiers, being born in Italy might make sense.  I do find it interesting that the death record only names the mother as Jane Setter.  If she was a British subject born abroad and registered, the birth should appear at the GRO.  Also, if Joseph was stationed in the UK in 1851 (worldwide index 1851 census), then Jane should be somewhere in the UK as well.  There  won't be any additional records in Canada that you haven't already found.

His Boer War service record would seem  to be available so am wondering if you have them -- not seeing a reference to William unless it's on the marriage record in 1920. 

Interestingly, there was a William Elton, an actor, who appeared in various plays including being in Montreal in 1881 (from newspapers.com).

You may have this info, but here's his obituary from 1998:

When Ann married Richard McKinlay, her parents' first names were correct -- Hugh & Agnes, but Bertram was her mother's maiden name.