I had noticed the cross-eye in some characters, but never investigated the phenomenon in detail. Anyway, here is why it happens. I assumed that the character in rest pose looks straight forward, but some of them don't. The direction of the gaze is defined by the line from the eye helper to the eye target helper (the selected diamonds in the picture). Whereas the default character stares slightly inwards, the asian woman stares visibly outwards. Forcing her to look straight ahead gives a crossed-eyed look.
This could perhaps be regarded as a glitch in the modelling, or perhaps some people actually look that way. Anyway, I have committed a fix that should solve the problem. The left and right gaze bones (Gaze_L and Gaze_R) are no longer located in front of each eye, but along the lines of staring in rest pose. That seems to do the trick.
It is not really necessary to have separate controls to move the gaze. Just select the gaze bone and use the Transform > Location option in the N-panel.
EDIT: I tilted the gaze bones so they are now oriented along the stare line. A translation along local Y will hence move the bone towards or away from the eye.
