Thank you for your request.
Yes, you can buy the Swiss Travel Pass. You can find all the information here: sbb.ch/leisure-holidays
See the map of validity under the downloads. You can travel to Brig by train with this pass.
In Switzerland we have no obligation to reserve seats (except Panorama Express trains). This means that you can sit wherever you want with a valid ticket/pass (in the right class, of course.)
If you still want to make a reservation, you can do so here: sbb.ch/tickets
Have a nice day. Greetings ZoeS