How to have an effect show up in a certain part of the clip?

This sounds like a job for a duplicated layer in conjunction with either an animated mask or an animated track matte, either of which can isolate the glass in the scope, which you can then boost in brightness.

Since you're new to After Effects, I recommend that you work your way through the basic learning materials. If you do so, such tasks as this will be obvious to you, since you'll have the basic building blocks of compositing and animation.

BTW, here are a couple of videos in which I show how to have an effect only apply to one item in a scene:

- using Roto Brush

- using masks (manual rotoscoping) and motion tracking