Gilchrist was a brassfounder, Independent Labour Party supporter, and a personal friend to Keir Hardie. He owned a workshop and billiard room on Eglinton Street, which he converted into the Eglinton Electreum in 1911. His son, Alexander Muir Gilchrist (b. 1881), managed the Troon Picture Palace.
Source: William Stewart, J. Keir Hardie, a biography (London, 1921) https://archive.org/details/jkeirhardiebiogr00stewiala
Glasgow 1913 valuation rolls: http://www.theglasgowstory.com/images/TGSV19166.jpg