Which sleep stage produces irregular sharply peaked eye movements with an initial deflection usually lasting LESS than 500 msec?

The stage that produces irregular sharply peaked eye movements with an initial deflection usually lasting less than 500 milliseconds is actually associated with REM sleep. During REM (Rapid Eye Movement) sleep, the eyes exhibit rapid, jerky movements that are characterized by their irregularity and distinct peaks, which can indeed have a short duration.

In contrast, the other options represent different sleep states or wakefulness, where such rapid and irregular eye movements are not typically observed. For instance, Stage 3 refers to deep sleep characterized by slow wave patterns on EEG, and much less eye movement activity. Stage 1 is a light sleep stage where sleep is easily disturbed, and eye activity is minimal as the body transitions into deeper sleep. The Stage Wake is characterized by alertness and is not associated with the specific eye movement patterns described in the question.

Therefore, the correct identification of REM sleep as the stage producing the described eye movements highlights the unique characteristics of this sleep state that are crucial for understanding sleep architecture and its physiological correlates.