To elucidate the neurobiological basis of cognition, which is dynamic and evolving, various methods have emerged to characterise time-varying functional connectivity (FC) and track the temporal evolution of functional networks. However, given a selection of regions, many of these methods are based on modelling all possible pairwise connections, diluting a potential focus of interest on individual connections. This is the case with the hidden Markov model (HMM), which relies on region-by-region covariance matrices across all pairs of selected regions, assuming that fluctuations in FC occur across all investigated connections; that is, that all connections are locked to the same temporal pattern. To address this limitation, we introduce Targeted Time-Varying FC (T-TVFC), a variant of the HMM that explicitly models the temporal fluctuations between two sets of regions in a targeted fashion, rather than across the entire connectivity matrix. In this study, we apply T-TVFC to both simulated and real-world data. Specifically, we investigate thalamocortical connectivity, hypothesizing distinct temporal signatures compared to corticocortical networks. Given the thalamus' role as a critical hub, thalamocortical connections might contain unique information about cognitive processing that could be overlooked in a coarser representation. We tested these hypotheses on high-field functional magnetic resonance data from 60 participants engaged in a reasoning task with varying complexity levels. Our findings demonstrate that the time-varying interactions captured by T-TVFC contain task-related information not detected by more traditional decompositions.