My mistake was that it doesn't fit my description of songs that I heard as a kid. It was released in 1984.
The track I should have included was She's Gone, one of Hall & Oates' earliest hits. That one first came out on Abandoned Luncheonette in 1973, and was re-released as a single in 1976.
Abandoned Luncheonette has been recognized in recent years as a timeless classic. An interesting fact about that album: according to All Music, Bernard Purdie was one of the drummers.