Recently, video-based large language models (video-based LLMs) have achieved impressive performance across various video comprehension tasks. However, this rapid advancement raises significant privacy and security concerns, particularly regarding the unauthorized use of personal video data in automated annotation by video-based LLMs. These unauthorized annotated video-text pairs can then be used to improve the performance of downstream tasks, such as text-to-video generation. To safeguard personal videos from unauthorized use, we propose two series of protective video watermarks with imperceptible adversarial perturbations, named Ramblings and Mutes. Concretely, Ramblings aim to mislead video-based LLMs into generating inaccurate captions for the original videos, thereby degrading the quality of video annotations through inconsistencies between video content and captions. Mutes, on the other hand, are designed to prompt video-based LLMs to produce exceptionally brief captions, lacking descriptive detail. Extensive experiments demonstrate that our video watermarking methods effectively protect video data by significantly reducing video annotation performance across various video-based LLMs, showcasing both stealthiness and robustness in protecting personal video content.