Understanding the main factors contributing to individual differences in fluid intelligence is one of the main challenges of psychology. A vast body of research has evolved from the theoretical framework put forward by Cattell, who developed the Culture-Fair IQ Test (CFT 20-R) to assess fluid intelligence. In this work, we extend and complement the current state of research by analysing the differential and combined relationship between eye-movement patterns and socio-demographic information and the ability of a participant to correctly solve a CFT item. Our work shows that a participant's eye movements while solving a CFT item contain discriminative information and can be used to predict whether the participant will succeed in solving the test item. Moreover, the information related to eye movements complements the information provided by socio-demographic data when it comes to success prediction. In combination, both types of information yield a significantly higher predictive performance than each information type individually. To better understand the contributions of features related to eye movements and socio-demographic information to predict a participant's success in solving a CFT item, we employ state-of-the-art explainability techniques and show that, along with socio-demographic variables, eye-movement data. Especially the number of saccades and the mean pupil diameter, significantly increase the discriminating power. The eye-movement features are likely indicative of processing efficiency and invested mental effort. Beyond the specific contribution to research on how eye movements can serve as a means to uncover mechanisms underlying cognitive processes, the findings presented in this work pave the way for further in-depth investigations of factors predicting individual differences in fluid intelligence.