Many industrial assembly tasks involve peg-in-hole like insertions with sub-millimeter tolerances which are challenging, even in highly calibrated robot cells. Visual servoing can be employed to increase the robustness towards uncertainties in the system, however, state of the art methods either rely on accurate 3D models for synthetic renderings or manual involvement in acquisition of training data. We present a novel self-supervised visual servoing method for high precision peg-in-hole insertion, which is fully automated and does not rely on synthetic data. We demonstrate its applicability for insertion of electronic components into a printed circuit board with tight tolerances. We show that peg-in-hole insertion can be drastically sped up by preceding a robust but slow force-based insertion strategy with our proposed visual servoing method, the configuration of which is fully autonomous.