Actually, it's the first one "Meeting and Parting" that SonicTH was looking for;
The BGM was used when Brock and Misty said goodbye to Ash in the episode "Gotta Catch Ya Later," although the BGM was only properly released a few days ago on the soundtrack, "TV Anime Pocket Monsters Original Soundtrack Best 1997-2010 Vol. 2"
Heres a link to it without the crazy japanese guy at the end;
Hope I helped a little on that.