In 1912 nearly half a million people in Ireland and elsewhere signed the Ulster Covenant and the parallel Declaration for women, campaigning against Home Rule in Dublin. This record has recently been digitised, and the names of signatories can be searched online.
There are two Cavers references among the signatories: Samuel Cavers (b. 1865) from Hawick, Scotland, and his wife Christina. This couple also appear in the 1911 Irish census, one of the few census returns to survive for Ireland. They lived in Spamount, County Tyrone, and by 1911 had three young children.
All of the family were noted in the census as Presbyterian, and given that they were Presbyterians living in Northern Ireland it is not surprising that they were against Ireland breaking away from the United Kingdom.
Samuel Cavers was the son of my gggg-uncle James Cavers (1819-1892) who was beadle or church officer of the parish church of Wilton, in Hawick.
In other branches of my family tree I recently made great breakthroughs researching a great-grandmother born in Dublin in 1879. Her family were Roman Catholic and, unsurprisingly, the surviving family members in Ireland do not appear on the Ulster Covenant list. They were probably in favour of Irish Home Rule.