This study addresses the challenges faced by individuals with upper limb disadvantages in operating power wheelchair joysticks by utilizing the extended Function–Behavior–Structure (FBS) model to identify design requirements for an alternative wheelchair control system. A gaze-controlled wheelchair system is proposed based on design requirements from the extended FBS model and prioritized using the MosCow method. This innovative system relies on the user’s natural gaze and comprises three levels: perception, decision making, and execution. The perception layer senses and acquires information from the environment, including user eye movements and driving context. The decision-making layer processes this information to determine the user’s intended direction, while the execution layer controls the wheelchair’s movement accordingly. The system’s effectiveness was validated through indoor field testing, with an average driving drift of less than 20 cm for participates. Additionally, the user experience scale revealed overall positive user experiences and perceptions of the system’s usability, ease of use, and satisfaction.