We present a fully automated, two-stage modular glottal area segmentation framework for high-speed videoendoscopy (HSV) designed for accuracy, generalizability, and real-time playback. Our detection-gated pipeline combines a YOLOv8n glottis localizer with a U-Net segmenter; the localizer defines a tight crop to ensure a consistent field of view and gates the output to reduce spurious segmentations during glottal closure. The models were trained on the GIRAFE (N=600) and BAGLS (N=55,750) datasets. Cross-dataset portability was evaluated by benchmarking GIRAFE-trained models on the BAGLS test set without fine-tuning. In these evaluations, the pipeline achieved a Dice Similarity Coefficient (DSC) of 0.745 (87% of the in-domain ceiling). On in-distribution test sets, the system achieved DSCs of 0.81 (GIRAFE) and 0.856 (BAGLS), outperforming or competing with state-of-the-art methods. An exploratory clinical study of 40 subjects demonstrated that the glottal area Coefficient of Variation (CV distinguished healthy from pathological function (p=0.006). The system processes ~35 frames per second on commodity hardware, enabling interactive clinical review. This design supports uniform extraction of laryngeal kinematic measures across varying acquisition settings. Code, weights, and software are available at https://github.com/hari-krishnan/openglottal.