[music, maestro] "I'm dapper and drowsy and ready for sleep." [/music]
what on earth does dappled mean?

Per the dictionary dappled means "spotted; mottled (probably from Old Norse depill, spot, splash, diminutive of dapi, pool."

The most common usage (according to a quick scan of google) is the horse's coat having mottled or spootted markings, particularly the dapple-gray. "Dappled sunlight", a less-common phrase, would be for example sunlight through tree leaves: though indeed restfully beautiful, that beauty is not the inherent meaning of "dappled".

From which it would seem that the Simon & Garfunkel lyric uses the word "dappled" improperly, or perhaps one should say "with poetic license".