We propose a method that actively estimates contact location between a grasped rigid object and its environment and uses this as input to a peg-in-hole insertion policy. An estimation model and an active tactile feedback controller work collaboratively to estimate the external contacts accurately. The controller helps the estimation model get a better estimate by regulating a consistent contact mode. The better estimation makes it easier for the controller to regulate the contact. We then train an object-agnostic insertion policy that learns to use the series of contact estimates to guide the insertion of an unseen peg into a hole. In contrast with previous works that learn a policy directly from tactile signals, since this policy is in contact configuration space, it can be learned directly in simulation. Lastly, we demonstrate and evaluate the active extrinsic contact line estimation and the trained insertion policy together in a real experiment. We show that the proposed method inserts various-shaped test objects with higher success rates and fewer insertion attempts than previous work with end-to-end approaches. See supplementary video and results at https://sites.google.com/view/active-extrinsic-contact.