Cable-driven serpentine manipulators hold great potential in unstructured environments, offering obstacle avoidance, multi-directional force application, and a lightweight design. By placing all motors and sensors at the base and employing plastic links, we can further reduce the arm's weight. To demonstrate this concept, we developed a 9-degree-of-freedom cable-driven serpentine manipulator with an arm length of 545 mm and a total mass of only 308 g. However, this design introduces flexibility-induced variations, such as cable slack, elongation, and link deformation. These variations result in discrepancies between analytical predictions and actual link positions, making pose estimation more challenging. To address this challenge, we propose a physical reservoir computing based pose estimation method that exploits the manipulator's intrinsic nonlinear dynamics as a high-dimensional reservoir. Experimental results show a mean pose error of 4.3 mm using our method, compared to 4.4 mm with a baseline long short-term memory network and 39.5 mm with an analytical approach. This work provides a new direction for control and perception strategies in lightweight cable-driven serpentine manipulators leveraging their intrinsic dynamics.