Infrared small target detection (ISTD) remains challenging because tiny, low-contrast targets are easily overwhelmed by clutter, noise, or occlusion. Conventional single-frame and multi-frame detectors rely on bounding-box supervision, which specifies final target locations but offers little explicit guidance for prioritizing candidate regions or preserving weak-target evidence before localization. Task-driven visual search offers such guidance: top-down goals and visual evidence jointly form a spatial priority map that ranks candidate locations. Building on this principle, we propose Gaze-DETR, a bio-inspired detector that learns an internal priority map before localization. First, a priority head predicts a normalized priority map from image features. Second, Residual Priority-Guided Feature Modulation (RPFM) enhances high-priority responses while retaining multi-scale features. Finally, Priority-Guided Anchor Query Injection (PAQI) converts high-priority locations into decoder anchor queries. We train the priority head using three supervision schemes: box-derived Gaussian maps; real-gaze maps constructed from fixation-density maps; and transferred pseudo-gaze maps learned from gaze--box relations in paired annotations and applied to Anti-UAV410 training boxes. To support the latter two schemes, we construct TIR-UAV120-Gaze with paired detection and task-driven eye-tracking annotations. On TIR-UAV120-Gaze, Gaze-DETR achieves 85.76 mAP$_{50}$ and 88.77 F1 with box-derived supervision, and 86.18 mAP$_{50}$ and 89.00 F1 with real-gaze supervision. On Anti-UAV410, it achieves 87.06 mAP$_{50}$ and 90.90 F1 with box-derived supervision, and 87.08 mAP$_{50}$ and 90.43 F1 with transferred pseudo-gaze supervision. These results show that explicit spatial-priority learning provides pre-localization guidance complementary to bounding-box supervision across annotation settings and costs.

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