Social media is being increasingly weaponized by state-backed actors to elicit reactions, push narratives and sway public opinion. These are known as Information Operations (IO). The covert nature of IO makes their detection difficult. This is further amplified by missing data due to the user and content removal and privacy requirements. This work advances the hypothesis that the very reactions that Information Operations seek to elicit within the target social systems can be used to detect them. We propose an Interval-censored Transformer Hawkes (IC-TH) architecture and a novel data encoding scheme to account for both observed and missing data. We derive a novel log-likelihood function that we deploy together with a contrastive learning procedure. We showcase the performance of IC-TH on three real-world Twitter datasets and two learning tasks: future popularity prediction and item category prediction. The latter is particularly significant. Using the retweeting timing and patterns solely, we can predict the category of YouTube videos, guess whether news publishers are reputable or controversial and, most importantly, identify state-backed IO agent accounts. Additional qualitative investigations uncover that the automatically discovered clusters of Russian-backed agents appear to coordinate their behavior, activating simultaneously to push specific narratives.