Perception is thought to rely upon evolving activity within a recurrent, distributed thalamocortical network whose interconnections are modulated by bursts of ascending neuromodulatory neurotransmitters, such as noradrenaline. To test this hypothesis, we leveraged a combination of pupillometry, fMRI and recurrent neural network modelling of an ambiguous figures task. Qualitative shifts in the perceptual interpretation of an ambiguous image were associated with peaks in pupil diameter, an indirect readout of phasic noradrenergic bursts. Based on previous modelling work, we hypothesized that increases in neuromodulatory tone led to neural gain alteration so as to causally mediate perceptual switches. To test this hypothesis, we trained a recurrent neural network to perform an analogous perceptual categorisation task, and then manipulated the gain of the RNN to mimic the effect of neuromodulators, such as noradrenaline. As predicted, we observed an earlier perceptual shift as a function of heightened gain. Leveraging a low-dimensional readout of the RNN dynamics, and a measure of the energy landscape traversed by the dynamics, we developed two novel predictions: perceptual switches should co-occur with peaks in low-dimensional brain state velocity and with flattened energy landscape dynamics. We used whole-brain fMRI data to confirm these predictions. These results confirm the core role of the neuromodulatory system in the large-scale network reconfigurations that mediate perceptual switches.