A key challenge in dexterous non-prehensile manipulation lies in dynamic finger gaiting—the sequential repositioning of fingers to achieve continuous object motion. The pen-spinning task, requiring precise, sequential multi-finger coordination without a stable grasp, serves as an ideal testbed for investigating such gaiting. Prior work, often limited by hand morphology, has typically yielded simpler policies reliant on fingertip balancing rather than dynamic finger gaiting. In this work, we investigate learning finger gaiting on an anthropomorphic hand in simulation. However, achieving this skill through reinforcement learning (RL) introduces significant challenges, particularly in policy exploration and the processing of complex observations. To address these, our framework employs waypoint-guided initialization and utilizes normalized contact forces as a form of privileged information during training. Our simulation results demonstrate the emergence of dynamic finger gaiting, enabling the efficient execution of the pen-spinning task. This work thereby establishes a viable methodology for acquiring complex coordination skills on high-degree-of-freedom (DoF) anthropomorphic hands.