Engagement influences participation, progression and retention in game-based e-learning (GBeL). Therefore, GBeL systems should engage the players in order to support them to maximize their learning outcomes, and provide the players with adequate feedback to maintain their motivation. Innovative engagement monitoring solutions based on players' behaviour are needed to enable engagement monitoring in a non-disturbing way, without interrupting the game-play and game flow. Furthermore, generic metrics and automatic mechanisms for their engagement monitoring and modelling are needed. One important metric that was used for engagement modelling is TimeOnTask, which represents the duration of time required by the player to complete a task. This paper proposes ToTCompute (TimeOnTask Threshold Computation), a novel mechanism that automatically computes--in a task-dependent manner--TimeOnTask threshold values after which student engagement decreases with a given percentage from his initial level of engagement (e.g., after 2 min student engagement will fall with 10% from his initial level). In this way the mechanism enables engagement modelling at a higher granularity and further enables engagement-based adaptation in GBeL systems. ToTCompute makes use of game-playing information and EEG signals collected through an initial testing session. The results of an experimental case study have shown that ToTCompute can be used to automatically compute threshold values for the TimeOnTask generic engagement metric, which explains up to 76.2% of the variance in engagement change. Furthermore, the results confirmed the usefulness of the mechanism as the TimeOnTask threshold value is highly task-dependent, and setting its value manually for multiple game tasks would be a laborious process.