CCTV-based vehicle tracking systems face structural limitations in continuously connecting the trajectories of the same vehicle across multiple camera environments. In particular, blind spots occur due to the intervals between CCTVs and limited Fields of View (FOV), which leads to object ID switching and trajectory loss, thereby reducing the reliability of real-time path prediction. This paper proposes SPOT (Spatial Prediction Over Trajectories), a map-guided LLM agent capable of tracking vehicles even in blind spots of multi-CCTV environments without prior training. The proposed method represents road structures (Waypoints) and CCTV placement information as documents based on 2D spatial coordinates and organizes them through chunking techniques to enable real-time querying and inference. Furthermore, it transforms the vehicle's position into the actual world coordinate system using the relative position and FOV information of objects observed in CCTV images. By combining map spatial information with the vehicle's moving direction, speed, and driving patterns, a beam search is performed at the intersection level to derive candidate CCTV locations where the vehicle is most likely to enter after the blind spot. Experimental results based on the CARLA simulator in a virtual city environment confirmed that the proposed method accurately predicts the next appearing CCTV even in blind spot sections, maintaining continuous vehicle trajectories more effectively than existing techniques.