Designing user-adaptive search systems necessitates modeling the user's knowledge state during information seeking. Gaze data offers insights into cognitive processes during task-based reading. Despite its potential, cognitive perspectives have been insufficiently explored in the representation of the user's knowledge state when designing search systems. We reanalyzed an eye-tracking dataset and constructed mixed-effects user models to identify which measurements of gaze activities (i.e., gaze metrics captured by eye trackers) are reflective of the user. Our study's findings indicate that there are statistically significant correlations between gaze metrics that measure the variability of saccadic eye movement and search performance. The accuracy of answers has been significantly influenced by the interaction between the control of saccade trajectories, measured by the standard deviation of absolute saccadic directions and the difficulty of the search task. We discuss the implications of these findings for the design of search systems adaptable to the user's state of knowledge.