I solved this.
I added code to the child theme for a video header, and needed to update the code to allow video headers on category pages. It was checking on_page and on_single, but not on_category.
Adrian, your direction to remove the site-wide header and use featured images is the opposite of what we are trying to do. I want one header that appears on every page and post, including archive and category pages. It’s not appearing on archive and category pages right now, we want to fix that.
