Further information: I just found this statement on a web site about the Argylls:

"the Kilmarnock bonnet has a plain red and white dicing around the edge and a red woollen toorie on top."

-- http://www.theargylls.co.uk/dress.php

If you scroll down you'll see a picture of a ranker from the 1960's wearing No. 1 dress and a Kilmarnock bonnet.

T.