Artificial model swimmers offer a platform to explore the physical principles enabling biological complexity, for example, multigait motility: a strategy employed by many biomicroswimmers to explore and react to changes in their environment. Here, we report bimodal motility in autophoretic droplet swimmers, driven by characteristic interfacial flow patterns for each propulsive mode. We demonstrate a dynamical transition from quasiballistic to bimodal chaotic propulsion by controlling the viscosity of the environment. To elucidate the physical mechanism of this transition, we simultaneously visualize hydrodynamic and chemical fields and interpret these observations by quantitative comparison to established advection-diffusion models. We show that, with increasing viscosity, higher hydrodynamic modes become excitable and the droplet recurrently switches between two dominant modes due to interactions with the self-generated chemical gradients. This type of self-interaction promotes self-avoiding walks mimicking examples of efficient spatial exploration strategies observed in nature.