In this paper, we validate non-intrusive eyetracking and head-movement indicators for predicting workload (WL) to support an air traffic controller (ATCO) self-evaluation. This will allow, e.g., to open or close sectors under more accurate consideration of the individual's state, identifying over- and underload risk. We investigate n = 18 ATCOs during simulated working sessions with three varying traffic-load scenarios (light, moderate, heavy task load), adhering to a counterbalanced, within-subjects design. We apply non-intrusive eye tracking and the Cooper-Harper WL Rating Scale (CHS). Further, we employed a wearable electroencephalography (EEG) device optimized for monitoring WL. We evaluate the performance of five classical machine learning models across two distinct labeling tasks: CHS and EEG. For CHS labeling, the models achieve an accuracy of 84% (F1-score 72%) when classifying WL levels into three categories (low, medium, high), and 93% (F1-score 83%) when categorizing WL into two classes (low/medium, high). Similarly, for EEG labeling, the models achieve an accuracy of 86% (F1-score 77%) in the three-level WL classification and 96% (F1-score 84%) in the binary WL classification. With this, we display the potential of machine learning techniques in predicting ATCO WL solely based on eye-tracking and head-movement measures.