We develop a novel characterization of extremal dependence between two cortical regions of the brain when its signals display extremely large amplitudes. We show that connectivity in the tails of the distribution reveals unique features of extreme events (e.g., seizures) that can help to identify their occurrence. Numerous studies have established that connectivity-based features are effective for discriminating brain states. Here, we demonstrate the advantage of the proposed approach: that tail connectivity provides additional discriminatory power, enabling more accurate identification of extreme-related events and improved seizure risk management. Common approaches in tail dependence modeling use pairwise summary measures or parametric models. However, these approaches do not identify channels that drive the maximal tail dependence between two groups of signals -- an information that is useful when analyzing electroencephalography of epileptic patients where specific channels are responsible for seizure occurrences. A familiar approach in traditional signal processing is canonical correlation, which we extend to the tails to develop a visualization of extremal channel-contributions. Through the tail pairwise dependence matrix (TPDM), we develop a computationally-efficient estimator for our canonical tail dependence measure. Our method is then used for accurate frequency-based soft clustering of neonates, distinguishing those with seizures from those without.