The basic idea is to setup a rig to animate two textures on one object. In this case, I want to animate the eyes texture and the mouth texture for the head object. This can be done by utilizing the UV Warp Modifier but I discovered a couple of pitfalls.  (Please see the Tutorial by BornCG https://youtu.be/5NlvgMYZgaY to see how this works)

Problem 1: The scale of the controller square

The size the square must be 1 unit across and 1 unit high. It does't seem to matter what units of measurement the scene is using. It could be metric, imperial or standard Blender units. The scale also has to be 1, 1, 1, so will make sure the scale has been applied to the object.

Problem 2:  Attribute Node

I should be able to animate each texture with separating with a dedicated UV Warp modifier but the first UV Warp modifier seem to be affecting both textures on the object. Make sure to have the attribute node plugged into the UV node on each texture other wise the target bone will affect both UV maps instead of the desired map.

Here is the full tutorial by BornCG