We conduct laboratory experiments on spatial beauty contest games in Taiwan employing university students who read Chinese. We observe subject’s final choice, as well as their lookup pattern leading up to the decision captured by remote video-based eye-trackers, and analyze their entire reasoning process. We observe level-k and other types in our subjects just like in the literature, but we find no "top-left" level-k types (which start their reasoning from the top-left corner). We instead identify several smaller classes of omitted types, including "D-type" who play randomly but avoid dominated strategies (D0) or perform one round of deletion of dominated strategies and best response to the remaining strategies (D1). Interestingly, some of the D0 and D1 subjects have lookup patterns resemble level-k reasoning, but start from U0 (or U0') randomizing across one’s (or opponent’s) undominated strategies. The newly discovered, hard-to-find dominance subjects allow us to explore the reasoning process of deleting dominated strategies through eye-tracking data. Lastly, we develop machine learning methods (VBEM) and show how it performs better than traditional likelihood-based methods in simulated eye-tracking data, and provide more consistent classification in the actual field data.