Set up controller bones (I like them in their own Armature) and make sure the “deform” box in the bone properties panel is unchecked.
find it easier having the entire face moving around with the eye directional controller because I’m weird like that (and also they end up in odd places because of how I have the head controller).
On the mesh where the shape keys are, right click on the shape key that needs to be driven by the bone.
