Observability in engagements with bearings-only measurements is a crucial factor in a homing loop. Under collision course conditions, one does not have information on range, which may result in poor performance when employing guidance laws that require estimation of the target maneuver, such as augmented proportional navigation. Maneuvering away from the collision triangle can improve the performance of the engagement because, by altering the line of sight, the bearing measurement will return some insights on the range. This work is focused on the design criteria of the maneuver. Rather than trying to optimize the maneuver with respect to some cost function, one can start by analyzing the eigenvalues of the error covariance matrix of the Kalman filter in the homing loop, properly normalized. They give, in fact, a measure of the observability of the system. A new guidance strategy is proposed, which exploits the information from the eigenvalues in the framework of a pursuit evasion differential game. A comparison of the new strategy with the classic solution of the differential game on a set of Monte Carlo samples, indicates that the proposed solution improves the performance of the engagement in terms of miss distance.