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Humanoids are to date still limited in reliable interpretation of social cues that humans convey which restricts fluency and naturalness in social human-robot interaction (HRI). We propose a method to read out two important aspects of social engagement directly from the brain of a human interaction partner: (1) the intention to initiate eye contact and (2) the distinction between the observer being initiator or responder of an established gaze contact between human and robot. We suggest that these measures would give humanoids an important means for deciding when (timing) and how (social role) to engage in interaction with a human. We propose an experimental setup using iCub to evoke and capture the respective electrophysiological patterns via electroencephalography (EEG). Data analysis revealed biologically plausible brain activity patterns for both processes of social engagement. By using Support Vector Machine (SVM) classifiers with RBF kernel we showed that these patterns can be modeled with high within-participant accuracies of avg. 80.4% for (1) and avg. 77.0% for (2).