You can accomplish this by using nutcracker jaw with negative camera flappiness setting in the parameters. Does this resolve your issue?
An error occurred while saving the commentAustin Bowers commented
So one character I've made is a mimic from dark souls. For those who don't know, a mimic is a living treasure chest with arms and legs, and a large mouth with sharp teeth.
This is what it looks like: https://vignette.wikia.nocookie.net/darksouls/images/a/a8/Mimic.png/revision/latest?cb=20130714135545
For this character's mouth to work, I am using the top part of the chest as the jaw, not the bottom like you would usually do. The problem is, for the mouth to be closed, mine has to be open.. can't really talk properly that way. So if the mouth was down when mine was closed, and move up when mine opens, that would be perfect.
The fix I have at the moment is a creative one, but not an efficient one. I named the top layers of the mouth +Left Eyebrow and +Right Eyebrow. So the mouth starts in the down position, and when I raise my eyebrows, the mouth opens. Problem fix... well that is if you don't mind talking a lot with your eyebrows, while also saying things with your mouth.
So, long story short an invert option would be nice here, and could help create more interesting characters for the future.