From memory, when it used to be the home side that changed kit, I'm pretty sure I have seen us change it against Arbroath, Dundee Utd, Aberdeen, Partick Thistle, Hearts, East Fife and Stenhousemuir (in a Scottish Cup game). I have a feeling we changed against Dumbarton when they had a predominately yellow shirt, but I might be misremembering that.
I'm sure we also changed against Albion Rovers in the Lanarkshire Cup.
The changes against Hearts, Dundee Utd and Aberdeen in particular didn't seem to be consistent and if you look on Youtube you'll see games against them where neither side changed and other games during the same period where a change was made.