The adaptive gain theory (AGT) posits that activity in the locus coeruleus (LC) is linked to two behavioral modes: exploitation, characterized by focused attention on a single task; and exploration, characterized by a lack of focused attention and frequent switching between tasks. Furthermore, pupil size correlates with LC activity, such that large pupils indicate increased LC firing, and by extension also exploration behavior. Most evidence for this correlation in humans comes from complex behavior in game-like tasks. However, predictions of the AGT naturally extend to a very basic form of behavior: eye movements. To test this, we used a visual-search task. Participants searched for a target among many distractors, while we measured their pupil diameter and eye movements. The display was divided into four randomly generated regions of different colors. Although these regions were irrelevant to the task, participants were sensitive to their boundaries, and dwelled within regions for longer than expected by chance. Crucially, pupil size increased before eye movements that carried gaze from one region to another. We propose that eye movements that stay within regions (or objects) correspond to exploitation behavior, whereas eye movements that switch between regions (or objects) correspond to exploration behavior.