Gestures help speakers and listeners during communication and thinking, particularly for visual-spatial information. Speakers tend to use gestures to complement the accompanying spoken deictic constructions, such as demonstratives, when communicating spatial information (e.g., saying “The candle is here” and gesturing to the right side to express that the candle is on the speaker's right). Visual information conveyed by gestures enhances listeners’ comprehension. Whether and how listeners allocate overt visual attention to gestures in different speech contexts is mostly unknown. We asked if (a) listeners gazed at gestures more when they complement demonstratives in speech (“here”) compared to when they express redundant information to speech (e.g., “right”) and (b) gazing at gestures related to listeners’ information uptake from those gestures. We demonstrated that listeners fixated gestures more when they expressed complementary than redundant information in the accompanying speech. Moreover, overt visual attention to gestures did not predict listeners’ comprehension. These results suggest that the heightened communicative value of gestures as signaled by external cues, such as demonstratives, guides listeners’ visual attention to gestures. However, overt visual attention does not seem to be necessary to extract the cued information from the multimodal message.