The vestibulocular reflex is triggered under normal conditions by signals (head rotated) from one or more of the three semicircular canals, one set (anterior+outer+posterior semicircular canal) on the right and one on the left side of the head.
The information from the semicircular canals is then distributed to the nuclei of the various external eye muscles using the vestibular nuclei and fasciculus longitudinalis medialis(FLM) as well as the nuclei of the brainstem that connect to the FLM. Due to the strong connection between the vestibular nuclei and the cerebellum, the cerebellum also has a decisive influence on the vestibuloocular reflex.
The task of the vestibulocular reflex is to keep the direction of gaze fixed when the head is rotated. The reflex triggers conjugated eye movements that compensate for the twists of the head.
The outer arch canal on the left side is activated when turning the head to the left. The endolymph then moves relatively to the right, triggering a conjugated eye movement to the right.
The outer arch canal on the right side is activated when you turn the head to the right. The endolymph then moves relatively to the left, triggering a conjugated eye movement to the left.
The two (hay+left) front semicircular canals are activated when you turn the head down (bend forward). The endolymph then moves relatively backwards/upwards, which triggers a conjugated eye movement upwards, "the gaze is raised".
The two (hay+left) posterior semicircular canals are activated when you turn the head backwards (stretching the neck). The endolymph then moves relatively forward/downward which triggers a conjugated eye movement downwards, "the gaze is lowered".
Usually, the head is rotated in different combinations of the above basic twists and the coupling system that then works inside the brain stem and cerebellum is astonishingly complex.
One can study the vestibuloculate reflex on oneself. For example, stand in front of a mirror. Fix the eye area in the mirror image of the face. Then turn your head in different directions. Notice that the eyes do not seem to touch but lie riveted in the mirror image even though the head can be allowed to spin wildly!