Rockin’ Back Inside My Heart, music by Angelo Badalamenti, lyrics by David Lynch, sung by Julee Cruise. Two uses film/TV. The first shown here is from Industrial Symphony No. 1: The Dream of the Broken Hearted from 1990. The second video, also from 1990, is a brilliant use of the song in episode 14 of Twin Peaks (the sound has some issues).

https://youtu.be/QmJzy0WrSXY
Julee Cruise – Rockin’ Back Inside My Heart – 1990

Julee Cruise – Rockin’ Back Inside My Heart – 1990 – Twin Peaks