Distractions external to a vehicle contribute to visual attention diversion that may cause traffic accidents. As a low-cost and efficient advertising solution, billboards are widely installed on side of the road, especially the motorway. However, the effect of billboards on driver distraction, eye gaze, and cognition has not been fully investigated. This study utilises a customised driving simulator and synchronised electroencephalography (EEG) and eye tracking system to investigate the cognitive processes relating to the processing of driver visual information. A distinction is made between eye gaze fixations relating to stimuli that assist driving and others that may be a source of distraction. The study compares the driver’s cognitive responses to fixations on billboards with fixations on the vehicle dashboard. The measured eye-fixation related potential (EFRP) shows that the P1 components are similar; however, the subsequent N1 and P2 components differ. In addition, an EEG motor response is observed when the driver makes an adjustment of driving speed when prompted by speed limit signs. The experimental results demonstrate that the proposed measurement system is a valid tool in assessing driver cognition and suggests the cognitive level of engagement to the billboard is likely to be a precursor to driver distraction. The experimental results are compared with the human information processing model found in the literature.