It has been widely recognized that human alertness is reflected in the eyes (e.g., when drowsiness, miosis, slow saccades, divergence, less compensatory vestibulo-ocular reflex, and less-accurate optokinetic response and smooth pursuit emerge). Previous studies that discovered these pupil/oculomotor anomalous behaviors along with lowering alertness evaluated only one or a few of them simultaneously, thus their emergence order is yet unknown. Presently, we focused on the following five pupil/oculomotor behaviors that can be evaluated under a natural stationary environment without giving external sensory stimulations: saccades, slow-phase eye movements, vergence, pupil diameter, and blinks. We demonstrate that their anomalous behaviors emerge in the following order: first: frequent saccades; second: slow saccades; third: divergence & miosis, then slow eye movement, while elongated eyelid closure duration emerges randomly in this sequence. These results provide a basis for the oculo-pupillometry-enabling objective monitoring of progressive drowsiness.