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Effective visual scanning and perception are essential to perform teleoperation construction tasks. In long-distance teleoperation systems, such as between Earth and the Moon, communication delays of at least 3 seconds impact operator performance and situational awareness, influencing eye movement patterns that vary with time-delay conditions and task types. This study examines features of eye movement patterns during time-delayed teleoperation tasks in lunar construction environment. We analyzed and quantified eye movement trajectories using recurrence quantification analysis to identify spatiotemporal patterns and gain insights into how operators interact with visual scenes under time-delayed and task-specific conditions. By visualizing these patterns, we interpreted their temporal and spatial characteristics and compared them in different situations. Our findings, which address a gap in understanding operator eye movement patterns during teleoperation tasks, have potential practical implications for improving visual perception by identifying quantitative patterns along with qualitative interpretations. This study will contribute to visual interface design in teleoperation systems for lunar construction, providing actionable insights for the design and operation of such systems.