Glass-insulated terminals (GITs) are widely used in high-reliability microelectronic systems, where glass fall-offs in the sealing region may seriously degrade the reliability of the microelectronic component and further degrade the device reliability. Automatic inspection of such defects is challenging due to strong light reflection, irregular defect appearances, and limited defective samples. To address these issues, a coarse-to-fine machine-learning framework is proposed for glass fall-off detection in GIT images. By exploiting the circular-ring geometric prior of GITs, an adaptive sector partition scheme is introduced to divide the region of interest into sectors. Four categories of sector features, including color statistics, gray-level variations, reflective properties, and gradient distributions, are designed for coarse classification using a gradient boosting decision tree (GBDT). Furthermore, a sector neighbor (SN) feature vector is constructed from adjacent sectors to enhance fine classification. Experiments on real industrial GIT images show that the proposed method outperforms several representative inspection approaches, achieving an average IoU of 96.85%, an F1-score of 0.984, a pixel-level false alarm rate of 0.55%, and a pixel-level missed alarm rate of 35.62% at a practical inspection speed of 32.18 s per image.