Doug,
When John was born in Scotland in 1895 there was no such thing as Irish citizenship. Britain and Ireland were all the one country until 1922. In terms of strict nationality, in 1895, he was just British. (Someone might perceive themselves as Scottish, English, Welsh or Irish but they were ethnic groups not a nationality. If they needed a passport the only one they could get was British).
Irish citizenship was created after 1922 and to be eligible, you either have to be born in any part of Ireland (including what is now Northern Ireland) or have a parent or grandparent born there. (It doesn't extend to great grand-parents). John had both parents & grandparents born in Ireland and so would certainly have been eligible for an Irish passport, once they had been invented. He would also still qualify for a British passport as well. Dual citizenship.
You are obviously curious as to why the couple went to Scotland. Ireland lacks natural resources. No coal, oil, iron ore etc, and so apart from a modest amount of shipbuilding in Belfast and the Belfast linen mills (which mostly only employed women), it did not really get the industrial revolution that benefited England and Scotland where mills, steelworks, ship building, coal mining and all their support industries were major employers creating hundreds of thousands of new jobs. Much better paid than subsistence farming or weaving. Added to that you had the effects of a massive population explosion in Ireland – up from 3 million in 1750 to 8 million in 1841 (no-one is really sure of the reasons why but reduced neo-natal deaths seem to be a factor) and the famine. So some push factors and some pull factors saw huge numbers of people leave Ireland. Something like 8 million people emigrated from Ireland between 1801 & 1921.
https://www.irish-genealogy-toolkit.com/emigration-Ireland-19th-century.html
If you look at the Scottish censuses for the Glasgow area in the late 1800s, you will see that about every fifth person recorded there was born in Ireland. Scotland was a particularly popular place to go to work because it was easy and very cheap to get to. Several sailings every day from Belfast. The shipping companies main business was cargo and the passengers were just top-up revenue. Competition was fierce and passenger fares very low. People working in Scotland could come home for weddings or the harvest, as well as holidays (Glasgow used to shut down for 2 weeks every July, known as the Glasgow Fair holiday and there would then be a huge exodus to Ireland). You could also send children back to stay with their grandparents, thereby leaving the wife free to work. You couldn’t do all those things so easily from Australia, America or Canada.
Scotland today is full of people of Irish descent. How they see themselves obviously varies from person to person but after 3 or 4 generations most see themselves as Scottish. But for someone whose parents were born in Ireland the link with Ireland would be much stronger. I’d guess that’s how it was for John born in Bellshill.