Appearance-based gaze estimation frequently relies on deep Convolutional Neural Networks (CNNs). These models are accurate, but computationally expensive and act as "black boxes", offering little interpretability. Geometric methods based on facial landmarks are a lightweight alternative, but their performance limits and generalization capabilities remain underexplored in modern benchmarks. In this study, we conduct a comprehensive evaluation of landmark-based gaze estimation. We introduce a standardized pipeline to extract and normalize landmarks from three large-scale datasets (Gaze360, ETH-XGaze, and GazeGene) and train lightweight regression models, specifically Extreme Gradient Boosted trees and two neural architectures: a holistic Multi-Layer Perceptron (MLP) and a siamese MLP designed to capture binocular geometry. We find that landmark-based models exhibit lower performance in within-domain evaluation, likely due to noise introduced into the datasets by the landmark detector. Nevertheless, in cross-domain evaluation, the proposed MLP architectures show generalization capabilities comparable to those of ResNet18 baselines. These findings suggest that sparse geometric features encode sufficient information for robust gaze estimation, paving the way for efficient, interpretable, and privacy-friendly edge applications. The source code and generated landmark-based datasets are available at https://github.com/daniele-agostinelli/LandmarkGaze.git.