Establishing common ground in remote cooperation is challenging because nonverbal means of ambiguity resolution are limited. In such settings, information about a partner's gaze can support cooperative performance, but it is not yet clear whether and to what extent the abundance of information reflected in gaze comes at a cost. Specifically, in tasks that mainly rely on spatial referencing, gaze transfer might be distracting and leave the partner uncertain about the meaning of the gaze cursor. To examine this question, we let pairs of participants perform a joint puzzle task. One partner knew the solution and instructed the other partner's actions by (1) gaze, (2) speech, (3) gaze and speech, or (4) mouse and speech. Based on these instructions, the acting partner moved the pieces under conditions of high or low autonomy. Performance was better when using either gaze or mouse transfer compared to speech alone. However, in contrast to the mouse, gaze transfer induced uncertainty, evidenced in delayed responses to the cursor. Also, participants tried to resolve ambiguities by engaging in more verbal effort, formulating more explicit object descriptions and fewer deictic references. Thus, gaze transfer seems to increase uncertainty and ambiguity, thereby complicating grounding in this spatial referencing task. The results highlight the importance of closely examining task characteristics when considering gaze transfer as a means of support.