It's a study from Ferdinando Carulli, from opus 241 (Ecole de Guitare).
Don't know exactly where it appears in the original, but you might find it here, if you're willing to do some searching.
And, fwiw, I find it a lovely piece. Delicate, simple, easy, without any frills. Just plain pretty, beautiful. I'm not a big Carulli fan, but he had his moments.
Here are dictionary definitions I found for the adjective "eclectic":
"deriving ideas, style, or taste from a broad and diverse range of sources"
(the first definition found in today's Google search for the word "eclectic")
"composed of elements drawn from various sources"
"selecting what appears to be best in various doctrines, methods, or styles"
Doing a quick Google search on your label information ("Hemosch Musikinstrumente") identifies this as an archtop guitar sold under his own label by instrument dealer Heinrich Moritz Schuster (HeMoSch), but likely manufactured at the Todt workshop: https://translate.google.com/translate?hl=en&sl=de&u=http://www.guitardoc-vintage.de/vintage-lounge-...
A quick whip up. It's in standard tuning (E2 A2 D3 G3 B3 E4). I don't claim it to be exactly as played but maybe it's good enough to get you started. The chords are just simple notes and to have something to aim at, and without the flageoletts/harmonics.
This is the best place to find if a musician has played a song live. It doesn't look like anyone recorded him playing it live. My guess - this song was recorded for the Super Mario Brothers movie, released in 1993. Also released in 1993: The Extremist. My guess would be that he recorded Speed of Light in late 1992 - maybe even as an extra track that never ...
For Roger Miller's Roger Miller album, that features the opening song River in the Rain, Discog credits:
Electric Guitar – Larry Byrom, Reggie Young
I would bet on Reggie Young since he's more reputed as a studio lead guitarist and has played with Merle Haggard for several albums, so your intuition was right.