The relationship between brain lateralization and cognitive functions is well-documented. The left hemisphere primarily handles tasks such as language and arithmetic, while the right hemisphere is involved in creative activities like drawing and music perception. Eye-tracking technology has shown the potential to reveal cognitive states by measuring ocular metrics such as pupil diameter and fixation duration. However, the ability to distinguish lateralized brain activity using these ocular metrics remains underexplored. Here, we demonstrate that pupil diameter and fixation duration can effectively classify left and right brain hemisphere activities. We obtained a considerably high classification performance, with an F1 score of 0.894. The results suggest that ocular metrics are robust indicators of lateralized brain activity and can be applied in cognitive monitoring and neurorehabilitation. Our future work expands on this by integrating these methods into real-time applications EyeBrain, potentially broadening their use across various cognitive and neurological domains.