As automated vehicles become more common, there is a need for precise measurement and definition of when and in what ways a driver can use a mobile phone in L2 autonomous driving mode, for how long it can be used, the complexity of the call content, and the accumulated mental workload. This study uses a 2 (driving mode) × 2 (call content complexity) × 6 (driving stage) three-factor mixed experimental design to investigate the effect of these factors on the driver's mental workload by measuring the driver's performance on Detection response tasks, pupil diameter, and EEG components in various brain regions in the alpha band. The results showed that drivers' mental workload levels converge between manual and automatic driving modes as the duration of driving increases, regardless of the level of complexity of the mobile phone conversation. This suggests that mobile phone conversations can also disrupt the driver's cognitive resource balance in L2 automatic driving mode, as it increases mental workload while also impairing the normal functioning of brain functions such as cognitive control, problem solving, and judgment, thereby compromising driving safety.