In summary:

The bottom row shows what happens after the head is pitched down by 90 deg. and the VOR is perfect; i.e. it keeps the eye still in space.

In the bottom row when the eye is looking right, the + is on the top of the eye. When the eye is looking at the center, the + is on the left side. Thus the eye is turned clockwise when looking right.

When the eye is looking left the + is on the bottom of the eye, that is turned counterclockwise relative to what it is at center.

Thus a simple pitch of the head will drive the eye position out of Listing's plane, clockwise when looking to the right and counterclockwise when looking to the left.

While the real eye never looks 90 deg. deg. to the side, even a small 10 deg. deviation has been found to produce a measurable torsional deviation from Listing's plane.