Welcome aboard, JP. Please take a moment and fill out your profile with your location, and edit your signature line to show your bike model and year.
I haven't seen a part that looks quite like that, but that doesn't mean much. Does your brake light work when you use the rear brake? You will get some other guys posting soon, so hang tight, as they might have better information for you.
In the meantime, here is the part fische for the right controls, so you can see how it goes together. #1 is the switch LINK
Joel in the Couve