Understanding the internal dynamics of Recurrent Neural Networks (RNNs) is crucial for advancing their interpretability and improving their design. This study introduces an innovative information-theoretic method to identify and analyze information-transfer nodes within RNNs, which we refer to as \textit{information relays}. By quantifying the mutual information between input and output vectors across nodes, our approach pinpoints critical pathways through which information flows during network operations. We apply this methodology to both synthetic and real-world time series classification tasks, employing various RNN architectures, including Long Short-Term Memory (LSTM) networks and Gated Recurrent Units (GRUs). Our results reveal distinct patterns of information relay across different architectures, offering insights into how information is processed and maintained over time. Additionally, we conduct node knockout experiments to assess the functional importance of identified nodes, significantly contributing to explainable artificial intelligence by elucidating how specific nodes influence overall network behavior. This study not only enhances our understanding of the complex mechanisms driving RNNs but also provides a valuable tool for designing more robust and interpretable neural networks.