Indirect vision through a mirror, while bi-manually manipulating both the mirror and another tool is a relatively common way to perform operations in various types of surgery. However, learning such psychomotor skills requires extensive training; they are difficult to teach; and they can be quite costly, for instance, for dentistry schools. In order to study the effectiveness of VR simulators for learning these kinds of skills, we developed a simulator for training dental surgery procedures, which supports tracking of eye gaze and tool trajectories (mirror and drill), as well as automated outcome scoring. We carried out a pre-/post-test study in which 30 fifth-year dental students received six training sessions in the access opening stage of the root canal procedure using the simulator. In addition, six experts performed three trials using the simulator. The outcomes of drilling performed on realistic plastic teeth showed a significant learning effect due to the training sessions. Also, students with larger improvements in the simulator tended to improve more in the real-world tests. Analysis of the tracking data revealed novel relationships between several metrics w.r.t. eye gaze and mirror use, and performance and learning effectiveness: high rates of correct mirror placement during active drilling and high continuity of fixation on the tooth are associated with increased skills and increased learning effectiveness. Larger time allocation for tooth inspections using the mirror, i.e., indirect vision, and frequency of inspection are associated with increased learning effectiveness. Our findings suggest that eye tracking can provide valuable insights into student learning gains of bi-manual psychomotor skills, particularly in indirect vision environments.