Occulomotor nerve (CN III) controls levator palpebrae so yes, the eyelids are controlled by cranial nerves.
number III. oculomotor
The third cranial nerve, the oculomotor is responsible for blinking and most other eyelid movement.
Cranial nerve III (CN3) is responsible for keeping the eye open. Cranial nerve VII (CN7) closes the eyelid.
The lateral rectus muscle is controlled by cranial nerve VI, also known as the abducens nerve. This muscle is responsible for moving the eye outward, away from the nose.
The cranial nerve associated with the eye is the oculomotor nerve (Cranial Nerve III). Damage to this nerve can result in symptoms such as ptosis (drooping of the eyelid), strabismus (misalignment of the eyes), and difficulties in eye movements, leading to double vision. Additionally, it can affect pupil constriction, resulting in a dilated pupil that does not respond to light.
The sternocleidomastoid and trapezius muscles are controlled by the accessory cranial nerve. Some call it cranial nerve XI.
Opening the eyes involves the cranial nerve called the oculomotor nerve (CN III). This nerve innervates the muscles responsible for raising the upper eyelid and controlling the pupil size.
The Olfactory nerve. CN1 Cranial Nerve I, or the first cranial nerve called the Olfactory nerve.
The vagus nerve is the 10th cranial nerve, also known as cranial nerve X.
The Optical nerver or the Second Cranial nerve controls and relays information absorbed through the rods and cones of the eye. Eye movements (eye muscles), however, are controlled by several other cranial nerves including the Oculomotor, Abducens, and Trochlear nerves.
Smell impulses are carried by the cranial nerve called the olfactory nerve (cranial nerve I). It is responsible for transmitting information about odors from the nose to the brain.
The optic nerve (cranial nerve II) is not involved in taste, as its primary function is vision. Taste is primarily mediated by the facial nerve (cranial nerve VII), glossopharyngeal nerve (cranial nerve IX), and vagus nerve (cranial nerve X).