Physiological signals such as pupil dilation and gaze velocity, recorded using eye-tracking devices, have been shown to be useful to characterise the different stages involved in information seeking processes. While most of the literature focuses on how eye-tracking signals relate to user satisfaction – such as perception of relevant search results – the use of eye-tracking data to infer users’ topic familiarity and query specificity during the formulation of information needs remains understudied. Topic familiarity reflects the user’s knowledge level, while query specificity indicates their search goal. By analysing pupil dilation and gaze velocity collected via a lab user study (N = 18), we achieved a Macro F1 score of 71.25% for predicting topic familiarity with a Gradient Boosting classifier, and a Macro F1 score of 60.54% with a k-nearest neighbours (KNN) classifier for query specificity. Furthermore, we developed a novel annotation guideline – specifically tailored for question answering – to manually classify queries as Specific or Non-specific. This study demonstrates the feasibility of using eye-tracking to better understand topic familiarity and query specificity in search.