Gaze stabilization is critical for enabling fluid, accurate, and efficient interaction in immersive augmented reality (AR) environments, particularly during task-oriented visual behaviors. However, fixation sequences captured in active gaze tasks often exhibit irregular dispersion and systematic deviations from target locations, a variability primarily caused by the combined effects of human oculomotor physiology, insufficient AR headset tracking and calibration accuracy, and environmental disturbances, undermining interaction performance and visual engagement. To address this issue, we propose TimeGazer, which reformulates gaze stabilization as a sequence-to-sequence temporal regression problem, predicting idealized fixation trajectories for the target-fixation phase from historical gaze dynamics in the search phase. We present a synthetic data generation and blending strategy that produces spatially concentrated, target-centered fixation references aligned with task objectives, substantially enriching the training space and enhancing model generalization. We train and evaluate TimeGazer on a hybrid dataset of real and augmented gaze sequences collected via Microsoft HoloLens 2 from 54 participants across multiple prediction horizons. Through the user study, statistical results demonstrate that TimeGazer significantly improves interaction accuracy and reduces completion time, confirming that temporal modeling of predictive gaze stabilization can strengthen attentional consistency and responsiveness in task-driven AR interaction. These findings highlight the broader potential of TimeGazer for advancing adaptive gaze-based interfaces and temporal modeling research in immersive systems.

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