This study presents a novel multi-stage hierarchical approach to optimize key selection on virtual keyboards using eye gaze. Existing single-stage selection algorithms have difficulty with distant keys on large interfaces. The proposed technique divides the standard QWERTY keyboard into progressively smaller regions guided by eye movements, with boundary fixations first selecting halves and quarters to sequentially narrow the search area. Within each region, keys are highlighted one by one for selection. An experiment compared the multi-stage approach to single-step techniques, having participants copy text using eye gaze alone under both conditions. Metrics on selection speed, words per minute, and usability ratings were significantly improved with the hierarchical technique. Half and quarter selection times decreased over 30% on average while maintaining accuracy, with overall task completion 20% faster. Users also rated the multi-stage approach as more comfortable and easier to use. The multi-level refinement of the selection area optimized interaction efficiency for gaze-based text entry.