Joint attention has been shown to be not only crucial for human-human interaction but also human-robot interaction. Joint attention can help to make cooperation more efficient, support disambiguation in instances of uncertainty and make interactions appear more natural and familiar. In this paper, we present an autonomous gaze system that uses multimodal perception capabilities to model responsive joint attention mechanisms. We investigate the effects of our system on people's perception of a robot within a problem-solving task. Results from a user study suggest that responsive joint attention mechanisms evoke higher perceived feelings of social presence on scales that regard the direction of the robot's perception.