An amorphous layer is commonly found at the interfaces of heterostructures due to lattice and thermal mismatch between dissimilar materials. While existing research has explored the impact of these layers on interfacial thermal transport, a comprehensive understanding of the underlying microscopic mechanisms remains essential for advancing thermal nanodevice development. Through phonon wave packet simulations, we investigated the dynamic behaviors of phonons crossing the amorphous interlayer at the GaN/AlN interface from the mode level. Our results highlight the amorphous layer's capability to notably adjust the polarization properties of incoming phonons, culminating in phonon localization. By examining transmission outcomes on a per-mode basis, we demonstrate the amorphous layer's impediment on phonon transport. Notably, this resistance escalates with an increase in the amorphous layer thickness (L), with certain high-frequency TA phonons showing unexpectedly high transmissivity due to polarization conversion and inelastic scattering at the amorphous interface. In addition, we observe that the amorphous layer prompts multiple reflections of incident phonons, instigating discernible from the two-beam interference equation. Finally, in pursuit of enhanced phonon transport, we employ annealing techniques to optimize the interface morphology, leading to the recrystallization of the amorphous layer. This optimization yields a substantial enhancement of interfacial thermal conductance by up to 38% for L = 3 nm.