Gaze-based assistive manipulation typically supports object selection, while arbitrary-position placement requires accurate spatial alignment between the headset and robot. However, for gaze-based manipulation, pose accuracy does not necessarily translate into task accuracy: translational and rotational errors jointly affect the transformed gaze ray and may compensate for each other. To study cross-device alignment from this task-oriented perspective, we present a markerless interaction framework and a dedicated cross-device dataset. We propose Graph-based Reference Selection to address sparse robot references. We further develop and benchmark multiple task-specific alignment pipelines under a unified protocol. Specifically, we introduce Gaze--Surface Intersection Error (GSIE), which directly measures the spatial error of the gaze-specified target. Experiments show that alignment methods ranked highly by conventional pose metrics are not always optimal in GSIE, demonstrating the importance of evaluating gaze-based manipulation at the task level.

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