Sleepiness and Excessive Daytime Sleepiness (EDS) are major public health concerns impacting the daily life and performances of subjects experiencing them. Usually measured by electroencephalographic measures or self-reported questionnaires, previous studies have shown that it is possible to measure them through voice analysis. In this article, we propose to investigate potential new vocal biomarkers of sleepiness and EDS on 93 patients affected by hypersomnia, namely reading pauses. We analyze the location and duration of the pauses annotated by a fully automated system and propose a new set of speech features. Based on these 12 descriptors, we have identified seven reading behavior profiles, that are almost fully explained by the physical and medical characteristics of the patients, including their level of EDS. Regarding short-term sleepiness, the observed differences are mainly due to the differences of texts and have a weak correlation with objective and subjective sleepiness measures.