Hi Stephen,
As mentioned in the other thread, the rigs are quite different. The Rig with the motion has no eye joints at all.
In this way, the eye joints are just moving along with the Rig that is connected.
The one eyeball seemed lost in my screen-capture, you can see it around the knees. Well, there are two spheres for each eye.
Typically, if the initial pose (T-pose, for example) is available, use it to reset the pose. This is usually done, by switching off the Skin, set the pose in the Weight tag, and Skin set to active again.
It was not set up correctly in the model I got. Which requires to delete the Weight, as well the Skin object. Place both Spheres tp the Joints for that specific eye and Bind both newly. Since it is only a single object with a Joint (Bn_Eye_L is used, and Be_Eye_L is not needed for the weighting), this is easily fixed as each vertex has 100% weight.
Perhaps just constrain the eyes to the Bn_Eye_L joint, (I would do the same for the right eye. You might need to set the Axis back into the middle (Mesh>Axis> Axis-Center> Reset)
Happy Holidays.
P.S.: I requested to check why I can’t sent you a PM, so far no reply. So, I can’t send you a link to a fixed model.