As generative AI becomes increasingly integrated into journalism, designing effective AI-use disclosures that inform readers without imposing unnecessary burden is a key challenge. While prior research has primarily focused on trust and credibility, the impact of disclosures on readers' attentional and cognitive load remains underexplored. To address this gap, we conducted a $3\times2\times2$ mixed factorial study manipulating the level of AI-use disclosure detail (none, one-line, detailed), news type (politics, lifestyle), and role of AI (editing, partial content generation), measuring load via NASA-TLX and eye-tracking. Our results reveal a significant attentional cost: one-line disclosures resulted in significantly higher fixation durations and saccade counts, particularly for AI-edited content. Detailed disclosures did not impose additional burden. Drawing on Information-Gap Theory, we argue that brief labels may trigger increased visual scrutiny by alerting readers to AI use without providing enough information. NASA-TLX scores and pupil diameter showed no significant differences across conditions, suggesting that AI-use disclosures do not impose cognitive burden regardless of the detail level. Interview insights contextualize these findings and reveal a strong preference for detailed or ``detail-on-demand'' designs. Our findings inform the design of gaze-informed adaptive disclosure interfaces that dynamically adjust transparency levels based on readers' attentional patterns and news context.

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