This paper presents results from the closed-loop characterization of an electrically coupled mode-localized sensor topology including measurements of amplitude ratios over a long duration, stability, noise floor, and the bandwidth of operation. The sensitivity of the prototype sensor is estimated to be -5250 in the linear operation regime. An input-referred stability of 84 ppb with respect to normalized stiffness perturbations is achieved at 500 s. When compared to frequency shift sensing within the same device, amplitude ratio sensing provides higher resolution for long-term measurements due to the intrinsic common-mode rejection properties of a mode-localized system. A theoretical framework is established to quantify noise floor associated with measurements validated through numerical simulations and experimental data. In addition, the operating bandwidth of the sensor is found to be 3.5 Hz for 3-dB flatness.