Pedestrian safety is a critical component of urban mobility and is strongly influenced by the interactions between pedestrian decision-making and driver yielding behavior at crosswalks. Modeling driver--pedestrian interactions at intersections requires accurately capturing the complexity of these behaviors. Traditional machine learning models often struggle to capture the nuanced and context-dependent reasoning required for these multifactorial interactions, due to their reliance on fixed feature representations and limited interpretability. In contrast, large language models (LLMs) are suited for extracting patterns from heterogeneous traffic data, enabling accurate modeling of driver-pedestrian interactions. Therefore, this paper leverages multimodal LLMs through a novel prompt design that incorporates domain-specific knowledge, structured reasoning, and few-shot prompting, enabling interpretable and context-aware inference of driver yielding behavior, as an example application of modeling pedestrian--driver interaction. We benchmarked state-of-the-art LLMs against traditional classifiers, finding that GPT-4o consistently achieves the highest accuracy and recall, while Deepseek-V3 excels in precision. These findings highlight the critical trade-offs between model performance and computational efficiency, offering practical guidance for deploying LLMs in real-world pedestrian safety systems.