Find pages_url for a project via the API to build a group landing page

I’m trying to build an RST index of all gitlab projects that have read the docs gitlab pages built. However, I can’t tell from the python API if a project has deployed pages. Constructing the links is easy, but I’ve found no way to test the private link in Gitlab EE (via token header, basic authentication, etc.) and no way to access the CI_PAGES_URL variable. How have other folks approached this?