Spatial researchers have been arguing over the optimum cognitive strategy for spatial problem-solving for several decades. The current article aims to shift this debate from strategy dichotomies to strategy flexibility--a cognitive process, which although alluded to in spatial research, presents practical methodological challenges to empirical testing. In the current study, participants' eye movements were tracked during a mental rotation task (MRT) using the Tobii ×60 eye-tracker. Results of a latent profile analysis, combining different eye movement parameters, indicated two distinct eye-patterns--fixating and switching patterns. The switching eye-pattern was associated with high mental rotation performance. There were no sex differences in eye-patterns. To investigate strategy flexibility, we used a novel application of the changepoint detection algorithm on eye movement data. Strategy flexibility significantly predicted mental rotation performance. Male participants demonstrated higher strategy flexibility than did female participants. Our findings highlight the importance of strategy flexibility in spatial thinking and have implications for designing spatial training techniques. The novel approaches to analyzing eye movement data in the current paper can be extended to research beyond the spatial domain.