The person who popularized "famous for being famous" was Angelyne.[1] Her boyfriend had a display printing business in LA, and, in 1984, arranged for billboards in LA, with just Angelyne and her picture. By 1995, over 200 billboards. She wasn't a movie star. Or a TV star. She'd done some singing. Yet she became famous.

[1] https://en.wikipedia.org/wiki/Angelyne