Resting-state functional magnetic resonance imaging (fMRI) is a well-established methodology to probe brain organization. Previous work has demonstrated that the probability of drowsiness and even sleep increases significantly in participants during resting-state. While it has been shown that such variations of conscious state are reflected by changes of activity in specific functional networks, it remains an open question whether and how the coupling between brain activity with the underlying structure is affected. By leveraging graph signal processing (GSP), we previously introduced a quantitative method to measure structure-function coupling. The spatial pattern of the structural decoupling index (SDI) corroborates the sensorimotor-association axis and carries information to identify individuals (fingerprinting), or decode different tasks. However, its temporal fluctuations have not yet been fully investigated. Here, we introduce a new time-resolved measure of SDI, as the instantaneous difference in amplitude between the structurally liberal and aligned portion of the fMRI signals, computed with structural connectome-informed GSP. A clustering step allows then to determine the recurrent patterns of SDI and how they differently express from the first to the second half of the acquisition. Using the two 15' resting-state sessions of 100 healthy individuals from the Human Connectome Project (HCP), we found that a global pattern of decoupling between brain structure and function is most characteristic for the first part, while a significant trend towards increased coupling, both globally and in sensory networks, occurs in the second half. This finding indicates higher SDI for higher level of alertness, versus increased coupling for higher drowsiness. The results are reliable across two sessions (test-retest) and are not present during motor task, where a higher degree of alertness is required throughout the whole acquisition. This work opens the avenue to analyze the dynamics of structure-function coupling, which have not been investigated so far.