Autonomous personal mobility vehicle (APMV) is a new type of small smart vehicle designed for mixed-traffic environments, including interactions with pedestrians. To enhance the interaction experience between pedestrians and APMVs and to prevent potential risks, it is crucial to investigate pedestrians' walking behaviors when interacting with APMVs and to understand the psychological processes underlying these behaviors. This study aims to investigate the causal relationships between subjective evaluations of pedestrians and their walking behaviors during interactions with an APMV equipped with an external human-machine interface (eHMI). An experiment of pedestrian-APMV interaction was conducted with 42 pedestrian participants, in which various eHMIs on the APMV were designed to induce participants to experience different levels of subjective evaluations and generate the corresponding walking behaviors. Based on the hypothesized model of the pedestrian's cognition-decision-behavior process, the results of causal discovery align with the previously proposed model. Furthermore, this study further analyzes the direct and total causal effects of each factor and investigates the causal processes affecting several important factors in the field of human-vehicle interaction, such as situation awareness, trust in vehicle, risk perception, hesitation in decision making, and walking behaviors.