Buena Vista Home Video was founded on February 13, 1987, but did not have an official logo on VHS until 1989.
Because there were not many installments owned by the Walt Disney Company that were not covered by the other Disney units, this logo is one of the hardest to find. One good example of finding this logo is the 1997 VHS of How the Toys Saved Christmas.
This is a very short-lived alternate logo, seen on Rockin' with the Chipmunks, part of the Alvin and the Chipmunks series.
This is the Buena Vista Home Video logo that appeared on Kiki's Delivery Service -- in fact, it appears twice, just like the 1986 Walt Disney Home Video logo appeared twice on Disney Sing Along Songs: Happy Haunting Party at Disneyland, which was released one week before Kiki's Delivery Service.
There were actually two variants of this logo -- the "Home Video" version and a new "Home Entertainment" version. The logo to the left was used in tandem with its 1998-2002 counterpart, and was seen on VHS tapes of Inspector Gadget (the DiC cartoon). The "Home Entertainment" variant began in 2002, but don't count on seeing it on the 2003 prints of the Miyazaki films; those DVDs and VHS tapes have the 2001 Walt Disney Home Entertainment logo.
Although current, it may still be an uncommon find. Try looking for a post-2006 print of a non-Disney and non-Touchstone film owned by the Walt Disney Company, either on DVD or Blu-ray Disc.
The music for this logo is the same as its 2002-2006 counterpart.