Brace Sleeve (BS) plays an essential role in connecting and fixing cantilevers of railway catenary systems. It needs to be monitored to ensure the safety of railway operations. In the literature, image processing techniques that can localize BSs from inspection images are proposed. However, the boxes produced by existing methods can contain incomplete and/or irrelevant information of the localized BS. This reduces the accuracy of BS condition diagnosis in further analyses. To address this issue, this paper proposes the use of an action-driven reinforcement learning method that adopts the coarse-localized box provided by existing methods, and finds the movements needed for the box to approach to the true BS position automatically and accurately. In contrast to the existing methods that predict one position of the box containing a BS, the proposed action-driven method sees the localization problem as a dynamic position searching process. The localization of BS is achieved by following a sequence of actions, which in this paper are position-moving (up, down, left or right), scale-changing (scale up or scale down) and shape-changing (fatter or taller). The policy of selecting dynamic actions is obtained by reinforcement learning. In the experiment, the proposed method is tested with real-life images taken from a high-speed line in China. The results show that our method can effectively improve the localization accuracy for 81.8% of the analyzed images. We also analyze cases where the method did not improve the localization and suggest further research lines.