I have finally figured out the connection between the two songs in my mind. Both were meant to be hits with a fat sound. The skinny sound vs the fat sound; new wave guitars vs the synth -- and the synth won out. In fact, it won everywhere starting with the DX7 and going into all areas of pop. The 1980s were known for synth and new drum sounds. How many synth bands were there? Depeche Mode, Eurythmics, Laurie Anderson, Human League, OMD, Pet Shop Boys, Joy Division, etc.
The skinny sound was more punk, new wave and Bill did it splendidly with Red Noise. But then things changed to a techno, keyboard sound. There were meandering "art" bands like Japan but mainstream tastes wanted Duran Duran who borrowed from Japan but were less pretentious, more straight ahead pop. The defining character were the keyboards. Even for the one-off hit bands like Talk Talk, The Art of Noise, Soft Cell, A-ha, Thomas Dolby, etc., the keyboards and sampling were the ticket. Even Peter Gabriel was known for a certain hollow flute keyboard sound.
So "Cars" came out in 1979 though I remember it from the early 1980s. "Flaming Desire" was also early 1980s and like I said they both had a hit quality -- i.e., a catchy melody -- with no overt guitar and a fatten keyboard sound. I remembered at the time that "Flaming Desire" was almost too fat, almost unwieldy thick, but listening to it now I don't have that impression. Still that old impression lingers. And that's why I associate it so strongly with "Cars." So I think I've solved my riddle concerning those two songs.
Now I'm working on "Are Friends Electric?" with Dali's footage from Hitchcock's Spellbound and another Crime Noir movie "Shed No Tears" with June Williams as the femme fatale. If Bill or anyone has any insight into this kind of psychological mixture of dream analysis and heartbreak, I would be glad to hear it.