The results of an experiment on the time-resolved spectral dynamics of the eosin phosphorescence in a low-temperature glycerol-water mixture are explained supposing a cluster structure of the supercooled liquid and the glass. An estimation of the size and the restructurization dynamics time of the clusters at about 237 K are performed. A modification concerning the procedure for the calculation of the relaxation function of a time-resolved spectral shift obtained in a supercooled liquid, possessing a cluster structure, is suggested. A conclusion on the existence of a new amorphous phase is inferred from the change in the spectral dynamics of the eosin phosphorescence observed in the low-temperature mixture.