Tired eyes get dry, and rubbing stimulates the lacrimal glands to produce more fluid. Tiredness also closes your eyes, so you may rub to keep them open. Finally, there's a connection between the muscles that move your eyes around and your heart. When these muscles are stimulated, a reflex slows the heart.
The American Academy of Pediatrics recommends screening for distance visual acuity, ocular alignment, and ocular media clarity for children 3 to 6 years of age and older.