I'm not aware, nor have I ever heard of using mute in the manner you describe by automating it since envelopes already do that so well.
In my mind, "mute" is something that a lot of the time is used creatively by feel in real time. So, automating mute is necessary.
The feature is screwy, especially with a controller. Trying to do it with a mouse will drive you batty..
I've had it work with padkontrol as a controller.
To the OP. Try the learn function on the right click mute.
It is pretty funky all the clicks you have to do before you actually can automate something.