Most eye tracking methods are light-based. As such they can suffer from ambient light changes when used outdoors. It has been suggested that ultrasound could provide a low power, fast, light-insensitive alternative to camera based sensors for eye tracking. We designed a bench top experimental setup to investigate the utility of ultrasound for eye tracking, and collected time of flight and amplitude data for a range of gaze angles of a model eye. We used this data as input for a machine learning model and demonstrate that we can effectively estimate gaze (gaze RMSE error of 1.021 ± 0.189 degrees with an adjusted R2 score of 89.92± 4.9).