This sounds to me like two songs, transitioning about halfway through:
First, "Just Because", which I think of as a "country" classic, but may actually have Hapa Haole origins (https://en.wikipedia.org/wiki/Just_Because_(Nelstone%27s_Hawaiians_song)). I don't know of Led recording commercially.
Second, "Sweet Georgia Brown", which I think is on "Force of Nature" with Mike Kaawa.
The black guitar is a Guild, one of the thin semi-acoustic electrics they built in the late 80s or early 90s. They did a few different models and I don't recall exactly which one Led uses.