In this paper, we focus on objectively measuring cognitive engagement using eye-tracking techniques. Specifically, we analyze both gaze-based and pupil-based eye movement data to assess attention and absorption—two key dimensions of cognitive engagement. These ocular behaviors serve as complementary indicators of cognition, providing a more comprehensive representation of cognitive engagement. Using these objective measures, we examine how navigation style influences cognitive engagement with an 18-page web-based medical decision aid (DA). Our findings demonstrate that evaluating cognitive engagement through the objective measures of attention and absorption offers a more holistic understanding of user engagement. Furthermore, because the system used in our study supports emotionally taxing decision-making, our results extend the measurement of cognitive engagement to contexts beyond those driven by affective states such as flow.