Emotion recognition from physiological signals remains challenging due to their non-stationary, noisy, and subject-dependent characteristics. This work presents, to the best of our knowledge, the first comprehensive application of liquid neural networks for EEG-based emotion recognition. The proposed multimodal framework combines convolutional feature extraction, liquid neural networks with learnable time constants, and attention-guided fusion to model temporal EEG dynamics with complementary peripheral physiological and personality features. Dedicated subnetworks are used to process EEG features and auxiliary modalities, and a shared autoencoder-based fusion module is used to learn discriminative latent representations before classification. Subject-dependent experiments conducted on the PhyMER dataset across seven emotional classes achieve an accuracy of 95.45%, surpassing previously reported results. Furthermore, temporal attention analysis provides interpretable insights into emotion-specific temporal relevance, and t-SNE visualizations demonstrate enhanced class separability, highlighting the effectiveness of the proposed approach. Finally, statistical analysis of temporal dynamics confirms that the network self-organizes into distinct functional groups with specialized fast and slow neurons, proving it independently tunes learnable time constants and memory dominance to effectively capture complex emotion artifacts.