Indoor localization systems face a fundamental trade-off between efficiency and responsiveness, which is especially important for emerging use cases such as mobile robots operating in GPS-denied environments. Traditional RTLS either require continuously powered infrastructure, limiting their scalability, or are limited by their responsiveness. This work presents Eco-WakeLoc, designed to achieve centimeter-level UWB localization while remaining energy-neutral by combining ultra-low power wake-up radios (WuRs) with solar energy harvesting. By activating anchor nodes only on demand, the proposed system eliminates constant energy consumption while achieving centimeter-level positioning accuracy. To reduce coordination overhead and improve scalability, Eco-WakeLoc employs cooperative localization where active tags initiate ranging exchanges (trilateration), while passive tags opportunistically reuse these messages for TDOA positioning. An additive-increase/multiplicative-decrease (AIMD)-based energy-aware scheduler adapts localization rates according to the harvested energy, thereby maximizing the overall performance of the sensor network while ensuring long-term energy neutrality. The measured energy consumption is only 3.22mJ per localization for active tags, 951uJ for passive tags, and 353uJ for anchors. Real-world deployment on a quadruped robot with nine anchors confirms the practical feasibility, achieving an average accuracy of 43cm in dynamic indoor environments. Year-long simulations show that tags achieve an average of 2031 localizations per day, retaining over 7% battery capacity after one year -- demonstrating that the RTLS achieves sustained energy-neutral operation. Eco-WakeLoc demonstrates that high-accuracy indoor localization can be achieved at scale without continuous infrastructure operation, combining energy neutrality, cooperative positioning, and adaptive scheduling.