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The 1901 census has 3 Patrick Brawleys shown as born Newmains and living in Cambusnethan. Years of birth are

Abt 1885 living at 12 Brown Street - parents James and Sarah

Abt 1892 living at 12 New Row - parents Peter and Catherine

Abt 1894 living at 3 Main Street - parents Daniel and Helen

I've just come across this post.  The Patrick Brawley from Brown Street is the uncle of the other two. His parents, James and Sarah, had 10 children and Patrick was the youngest. He was born in 1884. He emigrated to America before the war. His brother, Daniel also had 10 children, 5 of whom emigrated to Canada- Patrick being one of them.
Peter had 13 children. His son, Patrick died in Lanarkshire in 1970.
The brothers Daniel and Peter married sisters Helen (Ellen) and Catherine Keenan.