Among various approaches to eye tracking systems, light-reflection based systems with non-imaging sensors, e.g., photodiodes or phototransistors, are known to have relatively low complexity; yet, they provide moderately accurate estimation of the point of gaze. In this paper, a low-computational approach on gaze estimation is proposed using the Eye Touch system, which is a light-reflection based eye tracking system, previously introduced by the authors. Based on the physical implementation of Eye Touch, the sensor measurements are now utilized in low-computational least-squares algorithms to estimate arbitrary gaze directions, unlike the existing light reflection-based systems, including the initial Eye Touch implementation, where only limited predefined regions were distinguished. The system also utilizes an effective pattern classification algorithm to be able to perform left, right, and double clicks based on respective eye winks with significantly high accuracy. In order to avoid accuracy problems for sensitive sensor biasing hardware, a robust custom microcontroller-based data acquisition system is developed. Consequently, the physical size and cost of the overall Eye Touch system are considerably reduced while the power efficiency is improved. The results of the experimental analysis over numerous subjects clearly indicate that the proposed eye tracking system can classify eye winks with 98% accuracy, and attain an accurate gaze direction with an average angular error of about 0.93 °. Due to its lightweight structure, competitive accuracy and low-computational requirements relative to video-based eye tracking systems, the proposed system is a promising human-computer interface for both stationary and mobile eye tracking applications.