Using Lip Sync to trigger other events

I'm sure there's a way to properly do this, but I'm just not figuring it out. I have a puppet that spits on his "F's" and "S's". The spit is a four frame cycle so I don't want to just build it into the mouth shape in the mouth group. I'd like it to be above the mouth group, and play the cycle through, even if the actual mouth has moved on to another viseme. Does that make sense?

I tried setting up a separate mouth group with a Lip Sync behavior and only two visemes, F and S, but it doesn't want to recognize them for some reason. It's only picking up the initial mouth group and shapes. Thanks!