Reliability is the primary goal of driverless vehicle design. Redundant system design is the key to ensure the safety and reliability of driverless vehicles, so some driverless vehicles adopt standby-sparing system. The standby-sparing system is a kind of computer systems that solves the fault tolerance problem by using two processors: a primary processor and a spare processor. The primary processor is responsible for executing main tasks. The spare processor is responsible for executing backup tasks. The release time assignment for backup tasks, as a part of task scheduling, is an important technology in real-time standby-sparing systems. The selective scheduling for tasks with $(m,k)$-constraint (MKSS) is the state-of-the-art scheduling method for real-time tasks in standby-sparing systems. However, this method is inefficient in release time assignment for backup tasks. In this work, we propose an efficient release time assignment method that can reduce the number of inspecting points and terminate the enumeration once there appears a special inspect point. Theoretical analysis results show that the new method can improve the execution efficiency of the release time assignment without sacrificing the energy-saving effect of MKSS. A set of experiments is conducted to evaluate the execution efficiency of the new method, and the results show that, compared with the MKSS method, the new method can reduce about 98.7% time overhead for assigning release time for tasks.