Incorporating an autonomous auxiliary camera into robot-assisted minimally invasive surgery (RAMIS) enhances spatial awareness and eliminates manual viewpoint control. Existing path planning methods for auxiliary cameras track two-dimensional surgical features but do not simultaneously account for camera orientation, workspace constraints, and robot joint limits. This study presents AutoCam: an automatic auxiliary camera placement method to improve visualization in RAMIS. Implemented on the da Vinci Research Kit, the system uses a priority-based, workspace-constrained control algorithm that combines heuristic geometric placement with nonlinear optimization to ensure robust camera tracking. A user study (N=6) demonstrated that the system maintained 99.84% visibility of a salient feature and achieved a pose error of 4.36 $\pm$ 2.11 degrees and 1.95 $\pm$ 5.66 mm. The controller was computationally efficient, with a loop time of 6.8 $\pm$ 12.8 ms. An additional pilot study (N=6), where novices completed a Fundamentals of Laparoscopic Surgery training task, suggests that users can teleoperate just as effectively from AutoCam's viewpoint as from the endoscope's while still benefiting from AutoCam's improved visual coverage of the scene. These results indicate that an auxiliary camera can be autonomously controlled using the da Vinci patient-side manipulators to track a salient feature, laying the groundwork for new multi-camera visualization methods in RAMIS.