Binocular rivalry (BR) is an intriguing phenomenon in which conflicting images are presented, one to each eye, resulting in perceptual alternations between each image. The rate of BR has been proposed as a potential endophenotype for bipolar disorder because (a) it is well established that this highly heritable psychiatric condition is associated with slower BR rate than in controls, and (b) an individual’s BR rate is approximately 50% genetically determined. However, eye movements (EMs) could potentially account for the slow BR trait given EM anomalies are observed in psychiatric populations, and there has been report of an association between saccadic rate and BR rate in healthy individuals. Here, we sought to assess the relationship between BR rate and EMs in healthy individuals ( N = 40, mean age = 34.4) using separate BR and EM tasks, with the latter measuring saccades during anticipatory, antisaccade, prosaccade, self-paced, free-viewing, and smooth-pursuit tasks. No correlation was found between BR rate and any EM measure for any BR task ( p > .01) with substantial evidence favoring this lack of association (BF₀₁ > 3). This finding is in contrast to previous data and has important implications for using BR rate as an endophenotype. If replicated in clinical psychiatric populations, EM interpretations of the slow BR trait can be excluded.