A consumer depth sensor is calibrated for a room, not for the eye in near field. Eye-tracking needs infrared cameras and IR LEDs.
To track gaze in a headset, the instinct is to reuse a consumer depth sensor. It is the wrong tool, for a reason of scale.
Calibrated for the room
These sensors are designed to measure a scene at room scale: a body at two meters, a hand at one meter. Their resolution and minimum range are sized for those distances.
Eye-tracking works in near field, a few centimeters from the eye. The target is not a volume, it is the corneal reflection: a point glint on the surface of the eye. The depth sensor has neither the resolution nor the working distance for that.
The right sensor
The solution is optical and active. Infrared LEDs light the eye and create controlled glints on the cornea. Short-focal infrared cameras, placed very close, watch the pupil and those glints.
Gaze position is derived from the geometry between pupil and corneal glints. It is precise, fast and immune to visible light. The principle to keep: choose the sensor by the scale of measurement, not by its availability.