Understanding the impact of quantum computing on cryptography has become a critical area of research, affecting both public-key and symmetric-key cryptographic systems. In particular, periodic distinguishers based on Simon’s algorithm play a central role in quantum cryptanalysis of symmetric-key primitives. As the structures become more complex, manually constructing suitable periodic distinguishers has become increasingly difficult. To address this, at CRYPTO 2022, Canale et al. proposed the first exhaustive search tool for finding periodic distinguishers, but it sometimes suffers from too large search spaces on complex structures. Then, at FSE 2025, Xiang et al. established a link between periodic functions and truncated differentials, yet did not provide an automated search method. In this work, we develop the first automated search model specifically tailored for AND-RX ciphers, combining the symbolic representation proposed by Liu et al. with the truncated differential approach to identify periodic distinguishers. Our model successfully finds 7-, 8-, 9-, 11- and 13-round periodic distinguishers for the SIMON cipher and achieves 8-, 9-, and 11-round results on SIMECK, demonstrating the practical effectiveness of our approach. In addition, we observe that the validity of the periodic distinguishers proposed by Xiang et al. can be significantly affected by the choice of constants. Motivated by this observation, we conduct a detailed analysis of how constants influence the propagation of periodicity. It enables us to construct 8-, 9-, 10-, 12- and 14-round periodic distinguishers for SIMON, and 9-, -10 and 12-round periodic distinguishers for SIMECK under partial key conditions.