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Rapid eye movement (REM) sleep is increasingly understood as a heterogeneous state composed of two neurophysiologically distinct microstates: tonic REM and phasic REM. Phasic REM, defined by brief clusters of saccadic eye movements and transient cortical activation, has been linked to emotional memory consolidation, sensorimotor integration, and autonomic modulation. Despite its importance, automated quantification of phasic versus tonic REM remains uncommon, mainly because existing electrooculography (EOG) methods rely on fixed thresholds or generic wavelet families that do not accurately capture real saccade morphology in clinical polysomnography (PSG). This study introduces a fully automated framework for detecting phasic REM based on hybrid adaptive segmentation of a single EOG channel. The segmentation algorithm fuses median absolute deviation (MAD) amplitude-change detection with a morphology score derived from a custom saccade kernel built from manually verified EyeCon recordings. Segment boundaries are refined using local derivative extrema to improve temporal alignment. A supervised support vector machine (SVM) classifier further refines segment labels using features based on saccade morphology, including correlations with custom log-sigmoid templates and a morphology similarity measure. All segmentation and classification hyperparameters were optimized exclusively on controlled EyeCon datasets with precise ground-truth event markers. The final model was then applied without modification to 21 full-night clinical PSG recordings. Event-level analysis on EyeCon yielded 92.9% correct detections, with 5.3% fragmentation and 1.8% missed events. When aggregated into saccadic bursts, the resulting REM microstructure was physiologically consistent: phasic REM accounted for 31.8 ± 3.5% of REM duration, and tonic REM for 68.2 ± 3.5%. Additional EEG analysis confirmed increased beta and gamma power during phasic REM, supporting physiological validity. The proposed framework provides an interpretable, morphology-aware, and computationally efficient tool for large-scale REM microstructure research. Its single-channel design and external validation on clinical PSG recordings make it suitable for both retrospective analyses and future clinical applications.