The microscopic connections between solvation dynamics and the experimentally measured dynamic emission Stokes shift are explored by molecular dynamics simulation using the hydrated electron as a fully quantum mechanical probe. Solvent response functions are computed using the method of spectral reconstruction at various time resolutions for both fluorescence and stimulated emission and compared directly to the dynamic evolution of the underlying electronic energy gap. The first spectral moment proves to be a better choice of characteristic frequency than the spectral maximum, and iterative deconvolution is found to significantly improve the spectrally determined solvent response function. Use of the appropriate characteristic frequency at zero time to produce solvent response functions which do not start at unity further improves the agreement between the spectrally determined and microscopic solvent response functions.