Autonomous Personal Mobility Vehicles (APMVs) are designed to address the ``last-mile'' transportation challenge for everyone. When an APMV encounters a pedestrian, it uses an external Human-Machine Interface (eHMI) to negotiate road rights. Through this interaction, passengers also engage with the process. This study examines passengers' gaze behavior toward pedestrians during such interactions, focusing on whether different eHMI designs influence gaze patterns based on passengers' personality traits. The results indicated that when using a visual-based eHMI, passengers often struggled to perceive the communication content. Consequently, passengers with higher Neuroticism scores, who were more sensitive to communication details, might seek cues from pedestrians' reactions. In addition, a multimodal eHMI (visual and voice) using neutral voice did not significantly affect the gaze behavior of passengers toward pedestrians, regardless of personality traits. In contrast, a multimodal eHMI using affective voice encouraged passengers with high Openness to Experience scores to focus on pedestrians' heads. In summary, this study revealed how different eHMI designs influence passengers' gaze behavior and highlighted the effects of personality traits on their gaze patterns toward pedestrians, providing new insights for personalized eHMI designs.