The eyes are in constant movement to optimize the interpretation of the visual scene by the brain. Eye movements are controlled by complex neural networks that interact with the rest of the brain. The direction of our eye movements could thus be influenced by our cognitive activity (imagination, internal dialogue, memory, etc.). A given cognitive activity could then cause the gaze to move in a specific direction (a brief movement that would be instinctive and unconscious). Neuro Linguistic Programming (NLP), which was developed in the 1970s by Richard Bandler and John Grinder (psychologist and linguist respectively), issued a comprehensive theory associating gaze directions with specific mental tasks. According to this theory, depending on the visual path observed, one could go back to the participant's thoughts and cognitive processes. Although NLP is widely used in many disciplines (communication, psychology, psychotherapy, marketing, etc), to date, few scientific studies have examined the validity of this theory. Using eye tracking, this study explores one of the hypotheses of this theory, which is one of the pillars of NLP on visual language. We created a protocol based on a series of questions of different types (supposed to engage different brain areas) and we recorded by eye tracking the gaze movements at the end of each question while the participants were thinking and elaborating on the answer. Our results show that 1) complex questions elicit significantly more eye movements than control questions that necessitate little reflection, 2) the movements are not random but are oriented in selected directions, according to the different question types, 3) the orientations observed are not those predicted by the NLP theory. This pilot experiment paves the way for further investigations to decipher the close links between eye movements and neural network activities in the brain.