Response timing measures play a crucial role in the assessment of automated driving systems (ADS) in collision avoidance scenarios, including but not limited to establishing human benchmarks and comparing ADS to human driver response performance. For example, measuring the response time (of a human driver or ADS) to a conflict requires the determination of a stimulus onset and a response onset. In existing studies, response onset relies on manual annotation or vehicle control signals such as accelerator and brake pedal movements. These methods are not applicable when analyzing large scale data where vehicle control signals are not available. This holds in particular for the rapidly expanding sets of ADS log data where the behavior of surrounding road users is observed via onboard sensors. To advance evaluation techniques for ADS and enable measuring response timing when vehicle control signals are not available, we developed a simple and efficient algorithm, based on a piecewise linear acceleration model, to automatically estimate brake onset that can be applied to any type of driving data that includes vehicle longitudinal time series data. We also proposed a manual annotation method to identify brake onset and used it as ground truth for validation. R2 was used as a confidence metric to measure the accuracy of the algorithm, and its classification performance was analyzed using naturalistic collision avoidance data of both ADS and humans, where our method was validated against human manual annotation. Although our algorithm is subject to certain limitations, it is efficient, generalizable, applicable to any road user and scenario types, and is highly configurable.