Unlike handedness, sighting eye dominance, defined as the eye unconsciously chosen when performing monocular tasks, is very rarely considered in studies investigating cerebral asymmetries. We previously showed that sighting eye dominance has an influence on visually triggered manual action with shorter reaction time (RT) when the stimulus appears in the contralateral visual hemifield with respect to the dominant eye (Chaumillon et al. 2014). We also suggested that eye dominance may be more or less pronounced depending on individuals and that this eye dominance strength could be evaluated through saccadic peak velocity analysis in binocular recordings (Vergilino-Perez et al. 2012). Based on these two previous studies, we further examine here whether the strength of the eye dominance can modulate the influence of this lateralization on manual reaction time. Results revealed that participants categorized as having a strong eye dominance, but not those categorized as having a weak eye dominance, exhibited the difference in RT between the two visual hemifields. This present study reinforces that the analysis of saccade peak velocity in binocular recordings provides an effective tool to better categorize the eye dominance. It also shows that the influence of eye dominance in visuo-motor tasks depends on its strength. Our study also highlights the importance of considering the strength of eye dominance in future studies dealing with brain lateralization.