Endoscopic cameras attached to miniaturised snakelike continuum robotic arms can improve dexterity, accessibility, and visibility in minimally invasive surgical tasks. This steerable camera can expand the field of view and enhance the surgical experience with additional degrees of freedom. However, it also creates more control options that complicate human-machine interaction. This challenge presents an opportunity to develop novel human-machine control strategies using visual sensing to complement the dexterous actuation of a steerable surgical manipulator. This study presents a semi-autonomous controller to assist teleoperation by steering a camera such that it keeps an arbitrary target in the centre of the field of view, thus assisting in surveying different orientations about the target with imagebased information. Two controllers are proposed using classical image-based visual servoing techniques and optimal visual predictive control techniques. These techniques are simulated and validated on our robot SnakeRaven: a 3D-printed patient-specific end-effector attached to the RAVEN II surgical platform. Both systems, most notably the visual predictive approach, operated successfully with robustness to a lack of information about the target. A video demonstrating the main results of this paper can be found via https://youtu.be/fiUM9qYdl1U