Sound source localization is a critical problem in various fields, including communication, security, and entertainment. Binaural cues are a natural technique used by mammalian ears for efficient sound source localization. Spiking neural networks (SNNs) have emerged as a promising tool for implementing binaural sound source localization approaches. However, optimizing the topology and size of SNNs is crucial to reduce computational costs while maintaining accuracy. This paper proposes a real-time structure of a reservoir SNN (rSNN) called Adaptive-Resonance-Theory-based rSNN (ART-rSNN) for localizing sound sources in the time domain by integrating an energy-based localization method. The dataset used in this work is recorded by two different omnidirectional microphones from a real environment. The dataset includes various sound events such as speech, music, and environmental sounds. The proposed ART-rSNN architecture can dynamically adjust the location of its neurons to amplify estimated energy near the sound source, resulting in higher localization accuracy. Our proposed method outperforms several conventional and state of the art algorithms in terms of accuracy and is able to detect the front and back direction of azimuth angle. This work demonstrates the potential of dynamic neuron arrangements in SNNs for improving sound source localization in practical applications.