Models of combined eye-head gaze shifts all aim to realistically simulate behaviorally observed movement dynamics. One of the most problematic features of such models is their inability to determine when a saccadic gaze shift should be initiated and when it should be ended. This is commonly referred to as the switching mechanism mediated by omni-directional pause neurons (OPNs) in the brainstem. Proposed switching strategies implemented in existing gaze control models all rely on a sensory error between instantaneous gaze position and the spatial target. Accordingly, gaze saccades are initiated after presentation of an eccentric visual target and subsequently terminated when an internal estimate of gaze position becomes nearly equal to that of the target. Based on behavioral observations, we demonstrate that such a switching mechanism is insufficient and is unable to explain certain types of movements. We propose an improved hypothesis for how the OPNs control gaze shifts based on a visual-vestibular interaction of signals known to be carried on anatomical projections to the OPN area. The approach is justified by the analysis of recorded gaze shifts interrupted by a head brake in animal subjects, and is demonstrated by implementing the switching mechanism in an anatomically based gaze control model. Simulated performance reveals that a weighted sum of three signals; gaze motor error, head velocity and eye velocity, hypothesized as inputs to OPNs, successfully reproduces diverse behaviorally observed eye-head movements which no other existing model can account for.