Here are stills from two stop-motion music videos from the eighties: Giblets Animation's 1984 video for Jackie Wilson's Reet Petite and Aardman's 1987 video for Robert Parker's Barefootin'. Both songs were decades old by the time these videos were made, dating from 1957 and 1966 respectively.
The Number Ones of the Eighties blog has some interesting history on the Reet Petite video, relating how it originated as a personal project but ended up propelling the song into the charts two years after Wilson's death. Barefootin', meanwhile, is notable both for being an early work by Rex the Runt creator Richard Goleszowski and for containing what I believe to be the earliest Aardman in-joke - a spaceship baring a striking resemblance to the one flown by Wallace and Gromit (whose first film was still in development at the time and not released until two years later) appears towards the end.
What I find interesting about these videos is that they're both examples of animation for the sake of animation, particularly Reet Petite. Clearly, stop-motion still had a good deal of novelty value at the time, and a piece of animation devoted to the simple pleasures of putting a plasticine character through a series of transformations could still receive mainstream attention.