In recent years, the use of automation has been promoted in various systems such as automobiles, and the interaction between the system and user tends to decrease and be monotonous. Consequently, there is a concern that the arousal level of the user may decrease during work. In a semi-automatic system that requires user intervention in an emergency, performance degradation or accidents may occur because of the driver falling asleep. Therefore, an effective method of maintaining the arousal level must be established. Currently, the methods of stimulating the driver such as the presentation of siren sounds and injection of the scent of mint are being studied as the methods of maintaining the arousal level for automobile drivers. However, these methods of maintaining the arousal level via external stimulation have also suffered with challenges such as discomfort with the stimulation. In our previously conducted study, we proposed a method of maintaining the arousal level by presenting information that induced intrinsic motivation for maintaining the driving behavior in the driver; such a presentation might help maintain the arousal level. We aim to make such a method more applicable by optimizing the timing of the induction of intrinsic motivation.