Magnetic Resonance Sounding (MRS) is a geophysical method that provides direct information on subsurface water content and can complement traditional hydrological observations for model calibration. We develop a coupled hydrogeophysical framework by linking one-dimensional unsaturated flow with an MRS forward model to simulate a time-lapse MRS experiment during an infiltration event in the Strengbach headwater catchment in northeastern France. The geometry of the model is conditioned using insights on the porous medium thickness provided by seismic refraction tomography, in order to reduce model uncertainties related to the thickness of subsurface layers. We apply a Global Sensitivity Analysis (GSA) to quantify how uncertainty in hydrodynamic parameters affects MRS signals and their temporal evolution. The GSA combines variance-based Sobol indices with two other moment-based metrics (AMAE and AMAV) to characterize the sensitivity of both the mean and the variance of the MRS signal distributions. Using these complementary metrics provides a more robust assessment of parameter influence than Sobol indices alone. Our results identify the parameters which exert the strongest control on time-lapse MRS signals and reveal how their influence changes during the infiltration event. We also identify parameters whose uncertainties have insignificant contribution to MRS signals. These insensitive parameters are not expected to be precisely estimated with inverse modeling techniques based on MRS data. These insights clarify the potential and limitations of MRS data for constraining hydrological parameters in shallow mountain aquifers and demonstrate how the temporal evolution of MRS sensitivity can be exploited to optimize monitoring strategies during transient hydrological events.