Through in-class observations of teaching assistants (TAs) and students in the lab sections of a large introductory physics course, we study which TA behaviors can be used to predict student engagement and, in turn, how this engagement relates to learning. For the TAs, we record data to determine how they adhere to and deliver the lesson plan and how they interact with students during the lab. For the students, we use observations to record the level of student engagement and pretests and post-tests of lab skills to measure learning. We find that the frequency of TA-student interactions, especially those initiated by the TAs, is a positive and significant predictor of student engagement. Interestingly, the length of interactions is not significantly correlated with student engagement. In addition, we find that student engagement was a better predictor of post-test performance than pretest scores. These results shed light on the manner in which students learn how to conduct inquiry and suggest that, by proactively engaging students, TAs may have a positive effect on student engagement, and therefore learning, in the lab.