Two-stage warning system plays a critical role in guiding drivers to prepare for takeovers in conditional automated driving. However, the optimal time interval for this system, especially under different takeover request (TOR) modalities, remains unclear. A driving simulator experiment with 36 participants was conducted to investigate the effects of time interval and TOR modality of two-stage warning system on drivers' takeover responses from a multidimensional perspective. Each participant completed takeovers with four time intervals (3 s, 5 s, 7 s, and 9 s) and three TOR modalities (visual-only, auditory-only, and auditory-visual). Drivers' takeover performance, mental workload, situation awareness (SA), user experience, and eye movements during the takeover process were recorded. The results indicated that drivers showed faster and higher-quality takeovers as the time interval increased from 3 s to 9 s. Their ratings of satisfaction, usefulness, effectiveness, and safeness of the warning system showed the inverted U-shaped trends, with the 7 s as a turning point. The 7 s interval was also favored for drivers to regain sufficient SA while maintaining an appropriate mental workload, as evidenced by both subjective measures and eye-tracking metrics. This allowed drivers to adopt more focused visual strategies for the takeover after receiving TOR warning, thereby improving takeover performance. Additionally, the auditory-visual TOR was found to be the most effective across all measures, followed by the auditory-only TOR, and finally the visual-only TOR. No significant interaction effects between time interval and TOR modality were observed. In conclusion, regardless of TOR modality, the 7 s time interval was generally favored for young drivers with relatively limited driving experience for swift takeover responses, high takeover quality, sufficient SA, appropriate mental workload, and good satisfaction ratings. When the interval was extended to 9 s, drivers' takeover performance improved, but with the cost of reduced satisfaction and potential shift in visual attention from driving task to non-driving-related task. These findings had implications for the design and application of appropriate time interval of two-stage warning system for Level 3 automatic vehicles.