I have system simile tot he picture, these two parts are similar to gears (but they are not), and between the teeth there is a backlash. This backlash is not known and I need to estimate it.

There are two speed sensors on each part. The simplest way I thought about it, is to excite part 1 and then take the speed readings for part 2, and see when it starts to move, and based on the time gap that part 2 is not moving, I can estimate the backlash

However, this just a theory, and not sure if it will work experimentally, and not sure how to statistically analyze either discrete or continuous time data.

So, what are useful method to estimate the backlash for system like this?