Hello,
I want to add a control (ideally a button), to control which graph gets displayed.
Is there a way to do this on Looker?
Take a look at Drill actions. This might give you what you want.
Also, you can add a button to a dashboard and have it navigate to page, set filter values, and more. So you might design a separate page with the specific charts and information you want, and let users click a button to see that page.
Hope this helps!