Thank you for posting this. Always the top subject.
Two hemispheres doesn’t mean two conscious entities. One (left) is conscious and the right one gives an impression of consciousness. Yet there remains one OBSERVER reduced to left hemisphere.
What the right hemisphere does remains beyond control of the observer until he/she realizes for example some kind of wrongdoing from the right and invests consciously an effort to stop it.
So split brain doesn’t mean split consciousness. Just an exodus/reduction of consciousness to the left side.