Hidden state variables govern the dynamics of many complex physical systems but often remain inaccessible to average measurements. We show that spontaneous fluctuations provide direct access to their relaxation dynamics. Starting from a general Langevin description, we demonstrate that the spectrum of a coupled observable naturally separates into three independent physical ingredients: the microscopic stochastic forcing, the coupling to the observable, and a universal Debye-type relaxation kernel whose spectral corner yields the collective relaxation time. In adaptive conductors, where the hidden state controls electrical conductance rather than polarization, this relaxation governs both current fluctuations and the chemical inductive response, revealing a fluctuation–response correspondence based on the common relaxation dynamics of stationary nonequilibrium states. Applying the theory to halide perovskite memristors, we show that the relaxation of the conductance state accelerates below the macroscopic SET and RESET thresholds, establishing fluctuation spectroscopy as an early-warning probe of resistive switching. These results establish noise spectroscopy as a sensitive probe of metastable ionic–electronic dynamics in halide perovskite devices, with implications for resistive-memory reliability and the broader characterization of emerging energy materials.