We investigated 1) the need for calibration to measure eye movement symmetry in healthy controls and 2) the potential of eye movement symmetry to distinguish between healthy controls and patients. We analyzed fixations, smooth pursuits, saccades, and conjugacy measured by a Spearman correlation coefficient and utilized a linear mixed-effects model to estimate the effect of calibration. Healthy participants (n = 18) did not differ in correlations between calibrated and non-calibrated conditions for all tests. The calibration condition did not improve the linear mixed effects model (log-likelihood ratio test p = 0.426) in predicting correlation coefficients. Interestingly, the patient group (n = 17) differed in correlations for the DOT (0.844 [95% CI 0.602, 0.920] vs. 0.98 [95% CI 0.976, 0.985]), H (0.903 [95% CI 0.746, 0.958] vs. 0.979 [95% CI 0.971, 0.986]), and OKN (0.898 [95% CI 0.785, 0.958] vs. 0.993 [95% CI 0.987, 0.996]) tests compared to healthy controls along the x-axis. These differences were not observed along the y-axis. This study suggests that automated eye tracking can be deployed without calibration to measure eye movement symmetry. It may be a good discriminator between normal and abnormal eye movement symmetry. Validation of these findings in larger populations is required.