A method is presented for analyzing spectra that arise when the final state of the transition is a mixed eigenstate with respect to some zero-order basis, as occurs, for example, in vibronic coupling between two electronic manifolds. The method involves a Green's function approach that permits a direct de-diagonalization of the mixed eigenstates in circumstances where only one of the component states of the mixed eigenstate carries oscillator strength with respect to the initial state. Specific attention is focussed on the case where the perturbed level structure is discrete, i.e., the spacing between levels is in excess of their energy widths. The 1B3u-1Ag fluorescence excitation spectrum of pyrazine in the region of the electronic origin, measured at ultrahigh resolution, reveals such discrete level structure associated with singlet-triplet mixing. The method described is used to analyze the P(1) band in the pyrazine (S1-T1) ← S0 molecular eigenstate spectrum. The computation of the energies of the zero-order eigenstates and the associated coupling matrix elements is demonstrated to be efficient and accurate.