In joint action literature it is often assumed that acting together is driven by pervasive and automatic process of co-representation, that is, representing the co-actor's part of the task in addition to one's own. Much of this research employs joint stimulus-response compatibility tasks varying the stimuli employed or the physical and social relations between participants. In this study we test the robustness of co-representation effects by focusing instead on variation in response modality. Specifically, we implement a mouse-tracking version of a Joint Simon Task in which participants respond by producing continuous movements with a computer mouse rather than pushing discrete buttons. We have three key findings. First, in a replication of an earlier study we show that in a classical individual Simon Task movement trajectories show greater curvature on incongruent trials, paralleling longer response times. Second, this effect largely disappears in a Go-NoGo Simon Task, in which participants respond to only one of the cues and refrain from responding to the other. Third, contrary to previous studies that use button pressing responses, we observe no overall effect in the joint variants of the task. However, we also detect a notable diversity in movement strategies adopted by the participants, with some participants showing the effect on the individual level. Our study casts doubt on the pervasiveness of co-representation, highlights the usefulness of mouse-tracking methodology and emphasizes the need for looking at individual variation in task performance.