Multiple speckle diffusing wave spectroscopy (MSDWS) can be applied to measure spatially heterogeneous mechanical behavior in soft solids, with high sensitivity to deformation and both spatial and temporal resolution. In this paper, we discuss the mathematical approach behind the quantification of the deformation rate from MSDWS data and provide guidelines for optimizing the selection of experimental parameters in measurements. After validating the method in extensional tests on an elastomer, we provide an example of the potentiality of MSDWS by measuring the spatial distribution of the deformation rate during shear debonding of adhesive tapes. We quantitatively characterize the deformation rate distribution related to shearing and peeling under loading. A highly heterogeneous deformation rate distribution is observed, and time-dependent measurements reveal an increase in deformation localization hundreds of seconds before full debonding. This behavior, previously predicted by theory and simulation, is demonstrated here experimentally for the first time.