While existing query-based 3D end-to-end visual trackers integrate detection and tracking via the *tracking-by-attention* paradigm, these two chicken-and-egg tasks encounter optimization difficulties when sharing the same parameters. Our findings reveal that these difficulties arise due to two inherent constraints on the self-attention mechanism, i.e., over-deduplication for object queries and self-centric attention for track queries. In contrast, removing self-attention mechanism not only minimally impacts regression predictions of the tracker, but also tends to generate more latent candidate boxes. Based on these analyses, we present SynCL, a novel plug-and-play synergistic training strategy designed to co-facilitate multi-task learning for detection and tracking. Specifically, we propose a Task-specific Hybrid Matching module for a weight-shared cross-attention-based decoder that matches the targets of track queries with multiple object queries to exploit promising candidates overlooked by the self-attention mechanism and the bipartite matching. To flexibly select optimal candidates for the one-to-many matching, we also design a Dynamic Query Filtering module controlled by model training status. Moreover, we introduce Instance-aware Contrastive Learning to break through the barrier of self-centric attention for track queries, effectively bridging the gap between detection and tracking. Without additional inference costs, SynCL consistently delivers improvements in various benchmarks and achieves state-of-the-art performance with $58.9\%$ AMOTA on the nuScenes dataset. Code and raw results are available at .