The gaze cueing effect is the tendency for people to respond faster to targets appearing at locations gazed at by others compared to locations gazed away from by others. The effect is robust, widely studied, and is an influential finding within social cognition. However, much is still unknown about the cognitive processes that drive this effect. Formal evidence accumulation models provide the dominant theoretical account of the cognitive processes underlying speeded decision making but have never been applied to gaze cueing research and rarely to the study of social cognition more broadly. In this study, using a combination of individual-level and hierarchical computational modelling techniques, we applied Evidence Accumulation Models to gaze and arrow cueing data (four data sets total, n = 171, 139,001 trials) for the first time to 1) identify which cognitive mechanisms underlie the gaze cueing effect, and 2) see whether these processes could be considered the same as those that underlie arrow cueing effects. At the group level, people were best described by an attentional orienting mechanism rather than higher-order decision bias or information processing mechanisms. However, we found evidence for individual differences such that not everyone was best described by an attentional orienting mechanism. Further, the same people who were best described by an attentional orienting mechanism for gaze cues tended not to be best described by that same mechanism for arrow cues, suggesting these cueing effects may induce different responses within the same people – although we interpret this finding with caution.