Given the capabilities of modern high-performance missiles, efficient evasion maneuver strategies are crucial for enhancing UAV survivability. This paper addresses the integration of evasion strategies and maneuver timing for targeted UAVs. Firstly, a three-dimensional engagement scenario is modeled based on the relative motion mechanism. Subsequently, a fundamental evasion strategy focusing on large roll maneuvers and two-phase acceleration is developed. With the initiation timing of direct force control as the control variable, the formulation of a constrained optimization problem aimed at maximizing miss distance is fully articulated. While preserving the high fidelity of the established switching model, the feasible timing intervals and the optimal timing are determined through numerical optimization. Finally, simulation experiments are conducted focusing on omnidirectional attacks from the upper hemisphere. The results demonstrate that by implementing specific evasion maneuvers at optimal timing, the target successfully escapes the effective range of the proximity fuse, thus confirming the feasibility of the proposed evasion maneuver strategy and timing optimization method.