When people interact with each other, their brains synchronize. However, it remains unclear whether interbrain synchrony (IBS) is functionally relevant for social interaction or stems from exposure of individual brains to identical sensorimotor information. To disentangle these views, the current dual-EEG study investigated amplitude-based IBS in pianists jointly performing duets containing a silent pause followed by a tempo change. First, we manipulated the similarity of the anticipated tempo change and measured IBS during the pause, hence, capturing the alignment of purely endogenous, temporal plans without sound or movement. Notably, right posterior gamma IBS was higher when partners planned similar tempi, it predicted whether partners' tempi matched after the pause, and it was modulated only in real, not in surrogate pairs. Second, we manipulated the familiarity with the partner's actions and measured IBS during joint performance with sound. Although sensorimotor information was similar across conditions, gamma IBS was higher when partners were unfamiliar with each other's part and had to attend more closely to the sound of the performance. These combined findings demonstrate that IBS is not merely an epiphenomenon of shared sensorimotor information but can also hinge on endogenous, cognitive processes crucial for behavioral synchrony and successful social interaction.