Well, better late than never. After a bit of digging around with the Wayback Machine, I was able to find both versions of the music video, more or less exactly of how they looked like when they released on the internet back in 1999. Keep in mind that this was many years before YouTube. For what ever it is worth, enjoy: https://archive.org/details/Van_Halen_Once
Sidenote: while the video was officially released on the internet, people could actually request the video to be played on MTV and VH1. I’ve yet to find any evidence that the video was actually broadcast, if at all. If anyone can shed some light on the subject, that would be great.