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Algorithms for eye movement classification are separated into threshold-based and probabilistic methods. While the parameters of static threshold-based algorithms usually need to be chosen for the particular task (task-individual), the probabilistic methods were introduced to meet the challenge of adjusting automatically to multiple individuals with different viewing behaviors (inter-individual). In the context of conditionally automated driving, especially while the driver is performing various secondary tasks, these two requirements of task-and inter-individuality fuse to an even greater challenge. This paper shows how the combination of task-and interindividual differences influences the viewing behavior of a driver during conditionally automated drives and that state-of-the-art algorithms are not able to sufficiently adapt to these variances. To approach this challenge, an extended version of a Bayesian online learning algorithm is introduced, which is not only able to adapt its parameters to upcoming variances in the viewing behavior, but also has real-time capability and lower computational overhead. The proposed approach is applied to a large-scale driving simulator study with 74 subjects performing secondary tasks while driving in an automated setting. The results show that the eye movement behavior of drivers performing different secondary tasks varies significantly while remaining approximately consistent for idle drivers. Furthermore, the data shows that only a few of the parameters used for describing the eye movement behavior are responsible for these significant variations indicating that it is not necessary to learn all parameters in an online-fashion.