Current theoretical accounts on the oscillatory nature of sustained attention predict that entrainment via transcranial alternating current stimulation (tACS) at alpha and theta frequencies on specific areas of the prefrontal cortex could prevent the drops in vigilance across time-on-task. Nonetheless, most previous studies have neglected both the fact that vigilance comprises two dissociable components (i.e., arousal and executive vigilance) and the potential role of differences in arousal levels. We examined the effects of theta- and alpha-tACS over the right dorsolateral prefrontal cortex in both components of vigilance and in participants who differed in arousal level according to their chronotype and time of testing. Intermediate-types performed the vigilance tasks when their arousal level was optimal, whereas evening-types performed the vigilance tasks when their arousal levels were non-optimal. Both theta- and alpha-tACS improved arousal vigilance in the psychomotor vigilance task (PVT), whereas alpha-tACS, but not theta-tACS, improved executive vigilance in the sustained attention to response task (SART), and counteracted the typical vigilance decrement usually observed in this task. Importantly, these stimulation effects were only found when arousal was low (i.e., with evening-types performing the tasks at their non-optimal time of day). The results support the multicomponent view of vigilance, the relevance of heeding individual differences in arousal, and the role of alpha oscillations as a long-range cortical scale synchronization mechanism that compensates the decrements in performance as a function of time-on-task by exerting and maintaining cognitive control attributed to activation of the right dorsolateral prefrontal cortex.