Filter through a custom post type

I have a specific page template that looks different from the rest of my pages. On that page I have a custom sidebar that lists the equivalent of "tags" & "categories" for this CPT.

When one of these "tags" is selected, I want the layout to stay the same, using this template.

Would the proper/best way to set this up be to have a taxonomy-tags.php template? That mirrors my custom page template?