To drive safely, the driver must be aware of the surroundings, pay attention to the road traffic, and be ready to adapt to new circumstances. Most studies on driving safety focus on detecting anomalies in driver behavior and monitoring cognitive capabilities in drivers. In our study, we proposed a classifier for basic activities in driving a car, based on a similar approach that could be applied to the recognition of basic activities in daily life, that is, using electrooculographic (EOG) signals and a one-dimensional convolutional neural network (1D CNN). Our classifier achieved an accuracy of 80% for the 16 primary and secondary activities. The accuracy related to activities in driving, including crossroad, parking, roundabout, and secondary activities, was 97.9%, 96.8%, 97.4%, and 99.5%, respectively. The F1 score for secondary driving actions (0.99) was higher than for primary driving activities (0.93–0.94). Furthermore, using the same algorithm, it was possible to distinguish four activities related to activities of daily life that were secondary activities when driving a car.