Hybrid organic-inorganic perovskites (HOIPs) are promising candidates for next-generation photovoltaic materials. However, there is a debate regarding the impact of interactions between the organic center and the surrounding inorganic cage on the solar cell's high diffusion lengths. It remains unclear whether the diffusion mechanism is consistent across various halide perovskite families and how light illumination affects carrier lifetimes. The focus is on ion kinetics of (CH3NH3)PbX3 (X = Br, Cl) perovskite halide single crystals. Muon spectroscopy (mu+SR)is employed to investigate the fluctuations and diffusion of ions via the relaxation of muon spins in local nuclear field environments. Within a temperature range of 30-340 K, ion kinetics are studied with and without white-light illumination. The results show a temperature shift of the tetragonal-orthorhombic phase transition on the illuminated samples, as an effect of increased organic molecule fluctuations. This relation is supported by density functional theory (DFT) calculations along the reduction of the nuclear field distribution width between the phase transitions. The analysis shows that, depending on the halide ion, the motional narrowing from H and N nuclear moments represents the molecular fluctuations. The results demonstrate the importance of the halide ion and the effect of illumination on the compound's structural stability and electronic properties.