LiDAR-based 3D single object tracking (3D SOT) is a critical task in robotics and autonomous systems. Existing methods typically follow frame-wise motion estimation or a sequence-based paradigm. However, the two-frame methods are efficient but lack long-term temporal context, making them vulnerable in sparse or occluded scenes, while sequence-based methods that process multiple point clouds gain robustness at a significant computational cost. To resolve this dilemma, we propose a novel trajectory-based paradigm and its instantiation, TrajTrack. TrajTrack is a lightweight framework that enhances a base two-frame tracker by implicitly learning motion continuity from historical bounding box trajectories alone-without requiring additional, costly point cloud inputs. It first generates a fast, explicit motion proposal and then uses an implicit motion modeling module to predict the future trajectory, which in turn refines and corrects the initial proposal. Extensive experiments on the large-scale NuScenes benchmark show that TrajTrack achieves new state-of-the-art performance, dramatically improving tracking precision by 3.02% over a strong baseline while running at 55 FPS. Besides, we also demonstrate the strong generalizability of TrajTrack across different base trackers. Code is available at https://github.com/FiBonaCci225/TrajTrack.