Do you have any more help from the Irish records? Do you know when he left Ireland, did he have brothers or sisters? Did they come to the US, if so where?
He was born too early for the civil records, but what about his siblings? Were there other children born to this couple after 1865? Can you find them?
His mother's maiden name, according to his death record, is suspicious. I haven't seen it before, which doesn't mean much, but it doesn't show up anywhere in Ireland on Griffith's Valuation according to
https://www.johngrenham.com/surnames/. No Gilshaws either. Not a good sign. It might be mistranscribed.
Are you able to get a copy of the actual death record itself? Right now you only have familysearch's transcription of it. Their transcription of census records leaves a lot to be desired. The record might also tell you the informant who provided the information. If it looks like a son or daughter that will help. Some death records even give the relation.
Have you looked for Maguire or other variant spellings?
I had an aunt Theresa who was called Tiny, but she was also the smallest of the family, so I don't know if it was a nickname based on her given name or her size.
