I tried to add a featured image to one of the pages, and while it will let me select and add the image in edit mode, it’s not displaying on the page after I update it. The site has other locations where featured images are already in place, but those are all posts. Is the fact that this is a page instead of a post possibly the issue, and if so is there a PHP file edit that would enable them for use on pages?

I also tested adding one of the featured images that is already working on a post, but that also did not display on the page.

By default static pages don’t display featured images as they don’t need a uniform way of displaying content as posts do. You can add manually any media to any page by simply adding it to the content, so simply add the image to your page wherever you need it. With posts it’s different – there you need a uniform way of displaying posts, along with date, author, comments as well so they look good and logically uniform on the blog (post list) page. Hope that makes sense.
Good luck!