When you have an Inherent push block it seems it will only trigger a block trigger if it is inherent as well.
I have a screen that you blow the whistle which makes a block appear, which is inherently a flag 60, push horizontally, and when it appears it then must be pushed onto a floor switch.
When having just a block trigger flag placed over top of the switch it won't work, but if you name the switch a block trigger through it's inherent flag it will work.