Fast and unambiguous failure localization for shared risk link groups (SRLGs) with multiple links is essential for building a fully survivable and functional transparent all-optical mesh network. Monitoring trails (m-trails) have been proposed as an effective approach to achieve this goal. However, each m-trail traverses through each link by constantly taking a wavelength channel, causing a significant amount of resource consumption. In this paper, a novel framework of all-optical monitoring for SRLG failure localization is proposed. We investigate the feasibility of periodically launching optical bursts along each m-trail instead of assigning it a dedicated supervisory lightpath to probe the set of fiber segments along the m-trail, aiming to achieve a graceful compromise between resource consumption and failure localization latency. This paper defines the proposed framework and highlights the relevant issues regarding its feasibility. We provide theoretical justifications of the scheme. As a proof of concept, we formulate the optimal burst scheduling problem via an integer linear program (ILP) and implement the method in networks of all possible SRLGs with up to $d=3$ links. A heuristic method is also proposed and implemented for multiple-link SRLG failure localization, keeping all the assumptions the same as in the ILP method. Numerical results for small networks show that the scheme is able to localize single-link and multiple-link SRLG failures unambiguously with a very small amount of failure localization latency.