To my delight, I have now found my great-grandfather's date of death from the Calendar of Wills and Administrations, 1858-1920 at FamilySearch. It seems that John Biggins died on 11 June 1905 and that probate was granted to his son in 1907.
He was on the 1901 census but gone by 1911. I have never been able to find a registration of his death from 1901 to 1911 in Ballinrobe, where I would have expected to find it, or anywhere in Ireland and still cannot.
Has anyone any idea how the son could get probate granted in 1905 without proof that his father was dead?
Would some form of proof other than a death certificate have been acceptable?