Do eye's muscle share the same nerve?
Each eye is controlled separately. Three cranial nerves emerge at the brain for each eye to control the so called extraocular muscles. That we usually move both eyes in one direction is due to that our brain is trained that way. Nonetheless, we sometimes move each eye individually, for example when looking at an object that is very close to our face (convergence). I wonder that you have not noticed it on yourself, since it is a pretty common eye movement. Further, you can train your brain to perform other, rather unusual movements, as you can see in this video.