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This sounds interesting, although I'm not exactly sure what it means. By "parallax" are you referring to the head rotating around the Y axis?
the existing Parallax Strength parameter in the Face behavior moves the eyes, nose, & mouth around when you rotate your head around the X & Y axes. However, the Mouth Strength parameter currently defaults to zero, which makes it ignore the parallax result. If you set Mouth Strength to 100%, you'll see parallax for the mouth, but you'll also see it scale up & down as you open & close your mouth. This request is about making these things independent -- so you can have parallax movement on the mouth without scaling the mouth wen your own mouth opens & closes.
Note that for Parallax Strength to work best, you have to have eyes, nose, & mouth that Warp Independently. It's not a strict requirement, but you'll see warpy-pulling on those elements if they don't have their own mesh.
I agree: I would like the mouth to move with parallax, without deforming it.
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