As autonomous vehicles (AVs) are increasingly deployed on public roads, understanding their real-world behaviors is critical for traffic safety analysis and regulatory oversight. However, many data-driven methods lack interpretability and cannot provide verifiable explanations of AV behavior in mixed traffic. This paper proposes SVBRD-LLM, a self-verifying behavioral rule discovery framework that automatically extracts interpretable behavioral rules from real-world traffic videos through zero-shot large language model (LLM) reasoning. The framework first derives vehicle trajectories using YOLOv26-based detection and ByteTrack-based tracking, then computes kinematic features and contextual information. It then employs GPT-5 zero-shot prompting to perform comparative behavioral analysis between AVs and human-driven vehicles (HDVs) across lane-changing and normal driving behaviors, generating 26 structured rule hypotheses that comprises both numerical thresholds and statistical behavioral patterns. These rules are subsequently evaluated through the AV identification task using an independent validation dataset, and iteratively refined through failure case analysis to filter spurious correlations and improve robustness. The resulting rule library contains 20 high-confidence behavioral rules, each including semantic description, quantitative thresholds or behavioral patterns, applicable context, and validation confidence. Experiments conducted on over 1,500 hours of real-world traffic videos from Waymo's commercial operating area demonstrate that the proposed framework achieves 90.0% accuracy and 93.3% F1-score in AV identification, with 98.0% recall. The discovered rules capture key AV traits in smoothness, conservatism, and lane discipline, informing safety assessment, regulatory compliance, and traffic management in mixed traffic. The dataset is available at: svbrd-llm-roadside-video-av.