Eye movements during natural tasks are well coordinated with ongoing task demands and many variables could influence gaze strategies. Sprague and Ballard (2003) proposed a gaze-scheduling model that uses a utility-weighted uncertainty metric to prioritize fixations on task-relevant objects and predicted that human gaze should be influenced by both reward structure and task-relevant uncertainties. To test this conjecture, we tracked the eye movements of participants in a simulated driving task where uncertainty and implicit reward (via task priority) were varied. Participants were instructed to simultaneously perform a Follow Task where they followed a lead car at a specific distance and a Speed Task where they drove at an exact speed. We varied implicit reward by instructing the participants to emphasize one task over the other and varied uncertainty in the Speed Task with the presence or absence of uniform noise added to the car's velocity. Subjects' gaze data were classified for the image content near fixation and segmented into looks. Gaze measures, including look proportion, duration and interlook interval, showed that drivers more closely monitor the speedometer if it had a high level of uncertainty, but only if it was also associated with high task priority or implicit reward. The interaction observed appears to be an example of a simple mechanism whereby the reduction of visual uncertainty is gated by behavioral relevance. This lends qualitative support for the primary variables controlling gaze allocation proposed in the Sprague and Ballard model.