Vehicular ad-hoc networks (VANETs) hold great potential for improving traffic safety and efficiency. However, their development is impeded by issues related to information authenticity, integrity, and user privacy. Existing certificateless aggregate signature (CLAS) schemes aim to overcome the limitations of conventional Certificate Authorities and Private Key Generators. Yet these schemes still exhibit high computational costs, low efficiency, susceptibility to selective attacks, and an inability to trace illegal signatures. To address these challenges, we propose a new traceable privacy-preserving authentication scheme. It builds on an optimized lightweight SM2 signature mechanism and employs a two-tier verification architecture. This design reduces verification complexity to a constant level O(1) through random coefficient-based stratified signature aggregation, thereby effectively resisting selective attacks. For traceability, the scheme incorporates rapid node localization paired with binary recursive message set verification. This minimizes the complexity of error signature positioning to O(logN) and supports dynamic vehicle management. Security analysis shows that the scheme satisfies fundamental security requirements for VANETs. It outperforms existing state-of-the-art methods in both authentication and tracing efficiency, providing robust security and privacy for intelligent transportation systems.