Needle in a haystack, but I happen to have a John Brown as an in-law. Have you checked immigration records? (This information is from Scotland's People and the Ellis Island site.)
My John Brown married Janet Thomson on 17 October 1905. He was a gardener at Calderwood Castle in East Kilbride and she was a daughter of the estate manager. Witnesses were James Brown, coalminer and Elizabeth Brown (m.s. Mackie).
Don't have birth on him but Janet was born 1886. In March 1909 they migrated to the USA on the Columbia out of Glasgow. Two children: Margaret 2, and Elizabeth 9 Months. Destination: John Brown (father), Dumont, New Jersey, USA.