Mutual gaze is important to social interaction, and can also facilitate task performance. Previous work has assumed that staring at someone maximises mutual gaze. Eye-tracking is used to explore this claim, along with the relationship between mutual gaze and task performance. Two participants Instruction Giver (IG) and Instruction Follower (IF) communicated via avatars in Second Life to solve simple arithmetic tasks. There were two conditions: staring (the IG's avatar stared continuously at the IF); and not-staring, (IG's avatar looked at IF and task-relevant objects). Instead of maximising mutual gaze, constant staring actually showed evidence of decreasing eye contact within the dyad. Mutual gaze was positively correlated with task performance scores, but only in the not-staring condition. When not engaged in mutual gaze, the IF looked more at task-related objects in the not-staring condition than in the staring condition. Implications and possible future work on social interaction are discussed.