Eye-movements are the only directly observable behavioural signals that are highly correlated with actions at the task level, and proactive of body movements and thus reflect action intentions. Moreover, eye movements are preserved in many movement disorders leading to paralysis (or amputees) from stroke, spinal cord injury, Parkinson's disease, multiple sclerosis, and muscular dystrophy among others. Despite this benefit, eye tracking is not widely used as control interface for robotic interfaces in movement impaired patients due to poor human-robot interfaces. We demonstrate here how combining 3D gaze tracking using our GT3D binocular eye tracker with custom designed 3D head tracking system and calibration method enables continuous 3D end-point control of a robotic arm support system. The users can move their own hand to any location of the workspace by simple looking at the target and winking once. This purely eye tracking based system enables the end-user to retain free head movement and yet achieves high spatial end point accuracy in the order of 6 cm RMSE error in each dimension and standard deviation of 4 cm. 3D calibration is achieved by moving the robot along a 3 dimensional space filling Peano curve while the user is tracking it with their eyes. This results in a fully automated calibration procedure that yields several thousand calibration points versus standard approaches using a dozen points, resulting in beyond state-of-the-art 3D accuracy and precision.