Positioning is expected to be a core function in intelligent transportation systems (ITSs) to support communication and location-based services, such as autonomous driving, traffic control, etc. With the advent of low-cost reflective reconfigurable intelligent surfaces (RISs) to be deployed in beyond 5G/6G networks, extra anchors with high angular resolutions can boost signal quality and makes high-precision positioning with extended coverage possible in ITS scenarios. However, the passive nature of the RIS requires a signal source such as a base station (BS), which limits the positioning service in extreme situations, such as tunnels or dense urban areas, where 5G/6G BSs are not accessible. In this work, we show that with the assistance of (at least) two RISs and sidelink communication between two user equipments (UEs), these UEs can be localized even without any BSs involvement. A two-stage 3D sidelink positioning algorithm is proposed, benchmarked by the derived Cramér-Rao bounds. The effects of multipath and RIS profile designs on positioning performance are evaluated, and several scenarios with different RIS and UE locations are discussed for localizability analysis. Simulation results demonstrate the promising positioning accuracy of the proposed BS-free sidelink communication system in challenging ITS scenarios. Additionally, we propose and evaluate several solutions to eliminate potential blind areas where positioning performance is poor, such as removing clock offset via round-trip communication, adding geometrical prior or constraints, as well as introducing more RISs.