Bath-induced coherence transfer effects on a time- and frequency-resolved resonant light scattering spectrum is theoretically investigated using the Markoff master equation. According to Eberly and Wodkiewicz, a general expression for an experimentally observable spectrum in terms of a molecular response function is derived within the density matrix formalism. To generalize our previous results of the bath-induced coherence transfer which were derived based on a displaced harmonic oscillator model [Y. Ohtsuki and Y. Fujimura, J. Chem. Phys. 91, 3903 (1989)], an eigenstate basis is used to represent a relevant system for investigating characteristics of the transfer. By the present model, we clarify the dependence of the bath-induced coherence transfer on the energy-level structure of the intermediate states associated with the transfer, i.e., energy mismatch effects. It is shown that if the energy mismatch of these states is smaller than dephasing rates, the bath-induced coherence transfer occurs resonantly. In the other cases, the energy mismatch brings about a modulation in the time evolution of the superposition state created by the bath-induced coherence transfer, which strongly diminishes the efficiency of the transfer. The resonance condition is derived analytically and is confirmed by numerical calculations of quantum beats induced by the bath-induced coherence transfer. The possibility of very rapid dephasing of a quantum beat signal which cannot be explained in terms of dephasing rates is also shown, when the transition moments have such. values that give pi-phase-shifted quantum beats in bath-induced fluorescence.