Textual information search is not a homogeneous process in time, neither from a cognitive perspective nor in terms of eye-movement patterns, as shown in previous studies. Our objective is to analyze eye-tracking signals acquired through participants achieving a reading task aiming at answering a binary question: Is the text related or not to some given target topic? This activity is expected to involve several phases with contrasted oculometric characteristics, such as normal reading, scanning, careful reading, associated with different cognitive strategies, such as creation and rejection of hypotheses, confirmation and decision. To model such phases, we propose an analytical data-driven method based on hidden semi-Markov chains, whose latent states represent different dynamics in eye movements. Four interpretable phases were highlighted: normal reading, speed reading, information search and slow confirmation. This interpretation was derived using model parameters and scanpath segmentations. It was then confirmed using different external covariates, among which semantic information extracted from texts. Analyses highlighted a good discrimination of reading speeds by phases, some contrasted use of phases depending on the degree of relationship between text semantic contents and target topics, and a strong preference of specific participants for specific strategies. As another output of our analyses, the individual variability in all eye-movement characteristics was assessed to be high and thus had to be taken into account, particularly trough mixed-effects models. As a perspective, the possibility of improving reading models by accounting for possible heterogeneity sources during reading was discussed. We highlighted how analysing other sources of information regarding the cognitive processes at stake, such as EEG recordings, could benefit from the segmentation induced by our approach.