As a key technology for 6G, integrated sensing and communication (ISAC) is receiving considerable attention, and deploying a reconfigurable intelligent surface (RIS) can enhance both communication performance and sensing capability of ISAC by providing additional degrees of freedom. In this paper, we investigate a beam training framework for RIS-aided ISAC systems where beam alignment for a communication user equipment (UE) is conducted while simultaneously detecting a single target through its echo signal. Using codebooks constructed according to the principles of the 5G standard, we propose a partial search procedure that achieves low training overhead and mathematically show that this strategy is sufficient to identify a suitable codeword combination to serve the UE. By applying the auxiliary beam pair method, the target's angle information from the perspectives of the base station and RIS is obtained. Then, a high-accuracy closed-form localization is proposed based on the angle estimates, and we further extend the proposed technique to multi-target localization scenarios. Numerical results highlight the advantages of the proposed technique in the ISAC context, showing that the training procedure can effectively find a codeword combination and that the target localization technique outperforms the benchmarks.

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