Under Hans Eysenck's Three-Factor Model of personality (PEN Model—Psychoticism, Extraversion, and Neuroticism), upon deep analysis of their fundamental and neurophysiological bases, which major biological system or mechanism of the brain is considered responsible by Eysenck for determining the level of 'Extraversion'?

According to Hans Eysenck's personality theory, 'Extraversion' is primarily determined by the cortical arousal level of the Reticular Activating System (RAS) in the brain. Introverted individuals naturally have a high level of RAS arousal, so they avoid excessive sensory stimulation, whereas extraverted individuals have a lower level and actively seek external stimulation. For more information, you can check the Wikipedia reference.