Eye gaze is a fast and ergonomic modality for pointing but limited in precision and accuracy. In this work, we introduce BimodalGaze, a novel technique for seamless head-based refinement of a gaze cursor. The technique leverages eye-head coordination insights to separate natural from gestural head movement. This allows users to quickly shift their gaze to targets over larger fields of view with naturally combined eye-head movement, and to refine the cursor position with gestural head movement. In contrast to an existing baseline, head refinement is invoked automatically, and only if a target is not already acquired by the initial gaze shift. Study results show that users reliably achieve fine-grained target selection, but we observed a higher rate of initial selection errors affecting overall performance. An in-depth analysis of user performance provides insight into the classification of natural versus gestural head movement, for improvement of BimodalGaze and other potential applications.