Subjective perceptual experience is influenced not only by bottom-up sensory information and experience-based top-down processes, but also by an individual’s current brain state [1]. Specifically, our previous study [2] found increased prestimulus insula and intraparietal sulcus (IPS) activity before participants perceived an illusory Gestalt (global) compared to the non-illusory (local) interpretation in a bistable stimulus. That study provided only a snapshot of the prestimulus brain state that favors an illusory interpretation. In the current study, we tested the hypothesis that the neural machinery that biases perception towards the illusory interpretation immediately before the stimulus onset, is also predictive of an individual’s general tendency to perceive it, which remains stable over time. We examined individual differences in task-free functional connectivity of the insula and the IPS and related it to differences in the individuals’ duration of the two interpretations. We found stronger connectivity of the IPS with areas of the default mode network and with extrastriate areas to predict shorter local perceptual phases, i.e., a faster switch to an illusory percept, but no equivalent results for the insula. Our fundings suggest that the subjective experience of an external stimulus results from integrating sensory representations of the visual cortex and abstract representations of the default mode network, which is accomplished by the IPS.