Each spinal nerve root has a bunch of muscles it innervates, but the American Spinal Injury Association (ASIA) decided that these particular groups are the ones to test. There’s technically special positioning for the patient, the patient may or may not look like this.
I’ve been meaning to upload some sciencey study doodles for a while. Hopefully I can be reasonably diligent. Maybe.
The first one is internuclear opthalmopelegia, this is a specific type of gaze palsy that results from a lesion to the medial longitidinal fasciculus (MLF). It is seen in some patients with MS (though it can also happen as a result of a small stroke). In a left INO, your gaze to the left is fine, but when you try to look to the right, your right eye looks, but your left eye can’t go past the midline. You can still cross your eyes though (that’s a different pathway).