Brake light out on leer 100xq

Hello, this is likely a dumb question, but this is the first time I've had to deal with doing this. My top break light on my cap went out and in order to fix it, I have to get a whole new break light rather than replacing the bulb. How do I remove the old wiring from this harness effectively and how will the new wiring go in, do I just press it in until I hear a snap, or do I need a tool?

Here's the harness with the existing brake light wiring in it.


And here's what the new one will look like: