According to the Kirkintilloch Herald, Wednesday 18 July 1923, "Kirkintilloch Harp, as from Wednesday last, ceased to exist." The members discussed the financial situation, and decided was impossible to carry on.
It might be worthwhile taking out a month's subscription at the British Newspaper Archive which has the Kirkintilloch Herald, Gazette and Falkirk Herald online, all give good coverage to football in that area.