<p>Reservoir landslides are strongly influenced by reservoir water-level fluctuations and precipitation, yet their deformation responses are nonlinear and time-varying. This study used the Fujiapingzi landslide in the Xiluodu Reservoir area as the primary case, with the Liziping Village and Lugao Town landslides used for external validation. SBAS-InSAR was applied to derive time-series deformation, and grey relational analysis, continuous wavelet transform (CWT), and wavelet coherence (WTC) were integrated to identify dominant hydrological controls and lagged response characteristics. Reservoir water level was identified as the dominant hydrological factor, with a mean grey relational degree of 0.958, exceeding that of precipitation (0.830). Monitoring points in the front-to-middle part mainly exhibited medium- to long-period oscillations and clear lagged responses to reservoir water-level changes, with lags of approximately 10–35 days. Precipitation mainly induced delayed responses of approximately 30–60 days in the front-to-middle part and shorter responses of approximately 5–15 days in the rear part. Based on the wavelet-identified periodic background and hydrological lag characteristics, wavelet-guided features were constructed for displacement prediction. Comparative experiments using SARIMAX, TCN, RF, and LSTM showed that wavelet-guided feature construction improved the performance of most models, with RF achieving the best performance in the main case (R² = 0.958). External validation further indicates that the effectiveness of the proposed framework is strongly site-dependent. Overall, the results confirm that wavelet-informed periodic and hydrological features can effectively support reservoir landslide displacement prediction.</p>