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Metaverse can obscure the boundary between the physical and virtual worlds. Specifically, for the Metaverse in vehicular networks, i.e., the vehicular Metaverse, vehicles are no longer isolated physical spaces but interfaces that extend the virtual worlds to the physical world. Accessing the Metaverse via autonomous vehicles (AVs), drivers and passengers can immerse in and interact with 3D virtual objects overlaying views of streets on head-up displays (HUD) via augmented reality (AR). The seamless, immersive, and interactive experience rather relies on real-time multi-dimensional data synchronization between physical entities, i.e., AVs, and virtual entities, i.e., Metaverse billboard providers (MBPs). However, mechanisms to allocate and match synchronizing AV and MBP pairs to roadside units (RSUs) in a synchronization service market, which consists of the physical and virtual submarkets, are vulnerable to adverse selection. In this paper, we propose an enhanced second-score auction-based mechanism, named EPViSA, to allocate physical and virtual entities in the synchronization service market of the vehicular Metaverse. The EPViSA mechanism can determine synchronizing AV and MBP pairs simultaneously while protecting participants from adverse selection and thus achieving high total social welfare. We propose a synchronization scoring rule to eliminate the external effects from the virtual submarkets. Then, a price scaling factor is introduced to enhance the allocation of synchronizing virtual entities in the virtual submarkets. Finally, rigorous analysis and extensive experimental results demonstrate that EPViSA can achieve at least 96\% of the social welfare compared to the omniscient benchmark while ensuring strategy-proof and adverse selection free through a simulation testbed.