Hand Pose Estimation (HPE) is a fundamental technology for various applications such as AR/VR and robotics. In these applications, the visibility of each hand joint in the image is crucial for assessing the reliability of estimation results under occlusion. However, most existing HPE methods output joint positions without explicitly indicating their visibility. Although some methods account for occlusion or visibility, visibility estimation has mainly been used as an auxiliary signal for improving pose estimation. To our knowledge, per-joint hand visibility estimation has not been systematically studied as a standalone task. In this work, we propose Hand Visibility Detector, a model for estimating the visibility of individual hand joints, and present the first systematic investigation of visibility estimation as an independent task. We show that leveraging the prior knowledge of HPE models pretrained on large-scale data as a backbone yields high performance in this task. We further demonstrate the utility of Hand Visibility Detector on a downstream task of 3D hand pose annotation via multi-view triangulation of 2D keypoints, showing that visibility-weighted triangulation reduces reprojection error. Our method is released as a ready-to-use package, and the code and demo are available at https://github.com/ryhara/hand_visibility_detector .