Many goal-directed, as well as spontaneous everyday activities (e.g., planning, mind wandering) rely on an internal focus of attention. In this EEG-eye-tracking co-registration study, we investigated effects of attention direction on EEG alpha activity and various relevant eye parameters. We used an established paradigm to manipulate internal attention demands within tasks by means of conditional stimulus masking. Consistent with previous research, IDC involved relatively higher EEG alpha activity (lower alpha desynchronization) at posterior cortical sites. Moreover, IDC was characterized by greater pupil diameter (PD) and PD variance, more and longer blinks, and fewer microsaccades, fixations and saccades. These findings show that internal versus external cognition is associated with robust differences in several neurophysiological indicators that contribute to suppress task-irrelevant information processing at the neural and perceptual level. In a second line of analysis, we explored the intrinsic temporal covariation between EEG alpha activity and eye parameters during rest. This analysis revealed a positive correlation of EEG alpha power with PD especially in bilateral parieto-occipital regions. Together, these findings suggest that EEG alpha activity and PD represent time-sensitive indicators of internal attention demands and are part of a neurophysiological gating mechanism to shield internal cognition from irrelevant sensory information.