In camera-based 3D multi-object tracking (MOT), the prevailing methods follow the tracking-by-query-propagation paradigm, which employs track queries to manage the lifecycle of identity-consistent tracklets while object queries handle the detection of new-born tracklets. However, this intertwined paradigm leads the inter-temporal tracking task and the single-frame detection task utilize the same model parameters, complicating training optimization. Drawing inspiration from studies on the roles of attention components in transformer-based decoders, we identify that the dispersing effect of self-attention necessitates object queries to match with new-born tracklets. This matching strategy diverges from the detection pre-training phase, where object queries align with all ground-truth targets, resulting in insufficient supervision signals. To address these issues, we present HSTrack, a novel plug-and-play method designed to co-facilitate multi-task learning for detection and tracking. HSTrack constructs a parallel weight-share decoder devoid of self-attention layers, circumventing competition between different types of queries. Considering the characteristics of cross-attention layer and distinct query types, our parallel decoder adopt one-to-one and one-to-many label assignment strategies for track queries and object queries, respectively. Leveraging the shared architecture, HSTrack further improve trackers for spatio-temporal modeling and quality candidates generation. Extensive experiments demonstrate that HSTrack consistently delivers improvements when integrated with various query-based 3D MOT trackers. For example, HSTrack improves the state-of-the-art PF-Track method by $+2.3\%$ AMOTA and $+1.7\%$ mAP on the nuScenes dataset.