After some trial and error, I came up with this control.
The brass wires from the eyes are glued into flat losenges of 3mm plywood at the bottom. These are controlled by fitting between two tongue depressors. They can slide up and down independently of each other.
A piece of fishing line runs from an eye on the control through a hole in the neck and out to a wire loop on the movable part of the mouth.
The idea is to be able to twist the eyes back and forth, and slide the mouth up and down, at the same time. This solution should work pretty well.