We investigated the functions and mechanisms of non-goal-driven eye movements, which are defined as eye movements induced when looking at visual stimuli on a display without engaging in a specific task or looking at a display without any visual stimuli or tasks. In our experiment, participants were asked to perform a visual search task on a display, which was followed by a rest period in which stimuli remained on the display or all stimuli were erased. During the rest period, the participants were asked to only look at the displays without engaging in any visual or cognitive tasks. We mainly analyzed the gaze-shift patterns in both task and rest periods, in which eye movements were classified in accordance with the angles of saccade directions in two consecutive saccades. The results indicate a significant difference between goal-driven eye movements, which were observed in the task period, and nongoal- driven eye movements, which were observed in the rest period. Scanning gaze-shift patterns dominated the task period, and backward and corrective-saccade-like gaze-shift patterns dominated the rest period. The gaze-shift pattern was affected by the task-difficulty during the task period. From these findings, we propose a model describing the oculomotor system in terms of goal-driven and non-goal-driven eye movements. In this model, the engagement levels of top-down and bottom-up control change along with task difficulty and are affected by the gaze-shift patterns during a visual search task. Decoupling of top-down control from the oculomotor system during a rest period induces backward saccades, resulting in fixation around the central part of a display. Therefore, we suggest that non-goaldriven eye movements play a crucial role in maintaining the readiness of the oculomotor system for the next search task.