An outstanding challenge for consciousness research is to characterize the neural signature of conscious access independently of any decisional processes. Here we present a model-based approach that uses inter-trial variability to identify the brain dynamics associated with stimulus processing. We demonstrate that, even in the absence of any task or behavior, the electroencephalographic response to auditory stimuli shows bifurcation dynamics around 250-300 milliseconds post-stimulus. Namely, the same stimulus gives rise to late sustained activity on some trials, and not on others. This late neural activity is predictive of task-related reports, and also of reports of conscious contents that are randomly sampled during task-free listening. Source localization further suggests that task-free conscious access recruits the same neural networks as those associated with explicit report, except for frontal executive components. Studying brain dynamics through variability could thus play a key role for identifying the core signatures of conscious access, independent of report.