Gaze depth estimation presents a challenge for eye tracking in 3D. This work investigates a novel approach to the problem based on eye movement mediated by the vestibulo-ocular reflex (VOR). VOR stabilises gaze on a target during head movement, with eye movement in the opposite direction, and the VOR gain increases the closer the fixated target is to the viewer. We present a theoretical analysis of the relationship between VOR gain and depth which we investigate with empirical data collected in a user study (N=10). We show that VOR gain can be captured using pupil centres, and propose and evaluate a practical method for gaze depth estimation based on a generic function of VOR gain and two-point depth calibration. The results show that VOR gain is comparable with vergence in capturing depth while only requiring one eye, and provide insight into open challenges in harnessing VOR gain as a robust measure.