Pink Crows (lost music video animation; 1985)
Pink Crows was a cartoon band, created as a side project of the artist NOBODY. They released three singles in 1985, and later ended that same year.
The Music Video
According to the Japanese Wikipedia article for the band, animation company Sunrise was involved in the animation production, and an article about them in My Anime magazine's April 1985 issue shows many images that are believed to be taken from a music video of the band, though without any hard evidence that this is the case.