In this paper, we examine the feasibility of assessing air traffic controller (ATCO) workload (WL) using non-intrusive eye-tracking measures and machine learning (ML) algorithms. We concurrently acquire electroencephalography (EEG) data from a workloadoptimized wearable device and subjective WL assessments through self-reported Cooper-Harper scale (CHS) workload-rating scores, employing both as label variables. A sample of n = 18 ATCOs participate in simulated work sessions encompassing tasks designed to induce three distinct task-load levels: light, moderate, and heavy. We evaluate the performance of five classical ML models. Focusing on the best-performing models, we apply feature selection techniques to identify reduced sets of eye-tracking features. Starting with 58 features, we use a recursive elimination method based on permutation importance, aiming to determine the minimal feature set while also striving for improved performance. The outcomes yielded promising results in the realm of workloadlevel estimation, achieving 96% accuracy (f1-score=0.87) with 34 features for high workload prediction and 88% accuracy (f1-score=0.82) using 57 features in predicting 3 different levels of workload. We further reduced the feature sets to 6-13 features for different tasks with minimal impact on performance. We identified a \x93knee point\x94 as the optimal balance between model performance and dimensionality. Adding more features beyond this point did little to improve performance, but increased model complexity. These results indicate that even a small number (less than 10) of features can be sufficient for WL prediction.