I love that Alan Parsons song and video.  Most of my favorite videos come from a lot later.  I'm not sure all meet your criteria, David Bash, because in some cases I might just like the video as a short film and the music does a nice job of scoring the film.  Here is my top 10.

1. Sabotage - Beastie Boys (love the song love the video)
2. Weezer - Buddy Holly - Another Spike Jonze classic
3. Thriller (long format) - Michael Jackson
4. This Note's for You - Neil Young
5. Yankee Rose - David Lee Roth - It was hard to pick a Dave song.  They're all so funny.  I might have even picked hot for teacher.  But this one has the lady that says, "My doctor says I need to buy a  laxative."
6. Rockafeller Skank - Fat Boy Slim
7. Mexican Radio -  Wall of Voodoo.  My hands down winner for best old school MTV no budget video.  I love when Stan's face pops out of the beans.
8. Fight the Power - Public Enemy
9. Girls - Dwight Twilley - in Boston we had a broadcast music video channel called V-66 on UHF.   They played this video every day when I came home from school and I believe it really did a lot to shape me.  They must have had a rotation because they played Dwight Twilley, How Soon is Now?  by the Smiths and Come on Eileen every day at the same time for 6 months.  I always associate those songs with each other.
10. Rapture - Blondie - I thought Deb was so HOT when I was 10.  I thought she was twice as HOT when I was 12.

Special mention goes to the Scud Mt. Boys video Penthouse in the Woods.  Because I was in it.