We have measured first and second order statistics of the velocity of phase singularities v in evolving speckle patterns of microwave radiation transmitted through random quasi-1D samples as the frequency is swept and relate these to global statistics of speckle evolution. When v is normalized by the standard deviation of the fractional intensity change, the probability distribution and correlation function of v approach those for random Gaussian fields even for localized waves. Analogous results are found for transmitted intensity normalized by the total transmission. This provides a unified framework for the statistics of speckle evolution and intensity.