19 William Hag(g)arts were born in Scotland 1863-1873, of whom five were born in Dundee and one in Arbirlot, both places in Angus.
However in the 1881 census there is only one William Haggart born 1863-1783 in Dundee and still living in Scotland. This is the son of David Haggart and Janet Mowatt, born 17 May 1870. The Arbirlot one, son of David Haggart and Mary Livingston, is also in Dundee.
Scotland's People has four deaths of William Haggarts born 1863-1873 and died before 1881, but just two died in Angus. Only one of the two died in Dundee. You could get those two death certificates from SP, which would definitively eliminate at least two candidates.
Nine more William Haggarts born 1863-1873 died in Scotland after 1881, none of them in Angus. So your one has to be one of six remaining ones who did not die in Scotland. There is just one death in England and Wales of a possible candidate, who died in Anglesey, Wales in 1948 aged 77.
There were no William Haggarts born 1863-1873 in Scotland and in either the USA census of 1880 or the Canadian census of 1881.
The USA Census of 1940 lists the family as William, 70, born Scotland; wife Mary J, 62, born Canada, son Kenneth, 25, born Michigan; daughter-in-law Helen, 18, born Michigan; grandson, 1, born Michigan.
In 1920 the family consisted of William, 50, born Scotland, immigrated 1892, plus wife Mary J, 43, born Canada, and six sons, the eldest, William, 18, born in Canada.
A family in Sarnia, Lambton, Ontario in 1901 consists of William Haggart, born 22 June 1867, Scotland, with wife J Mary, born 16 June 1876, born somewhere I can't decipher in Ontario, and son William, born 22? February 1900, Sarnia. William Sr had immigrated to Canada in 1889 and was naturalised there the same year. I note with disappointment that none of the William Haggarts born in Scotland between 1863 and 1873 was born on 22 June.
There are three children in the Ontario birth records - Annie Isabella 1894, William James 1900, Ogle Anderson 1902. Do Canadian birth certificates tell you much about the parents? Do they tell you the date and place of the parents' marriage?
Can you get his Canadian naturalisation papers? What about the US - obviously they moved to Michigan around 1903, but did they become US citizens?