Hello Alex,
It seems that you got a Surface Pen with two buttons on the side. This pen works best with Surface 3 and Surface Pro 3. It would pair with your Surface Book 2, however, the two buttons on the side may not work since the pen isn't specifically designed for it. We'd suggest using Surface Pen with single long button (Works with Surface Pro 4 and later models) or newest Surface Pen with no clip (Works with Surface 3 and later models).
For additional information on how to use your Surface Pen, you can refer to this article.
If you would like me to provide additional advice, simply respond to this thread. I will get notified and I’ll reply to you as soon as I can.
Regards.