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The dog's name WAS Gypsy, and the chorus has a line like "you are my friend" in it. There's a song by that name on Sykes' first album (self-titled, Vanguard records, 1970-ish), but I can't find any more information on it than that. What's interesting is that the reference I found online said "trad/arr Sykes," so it could be a folk song. However, it doesn't sound like one to me, and finding a folk song about a dog or a folk song called "Gypsy" is like finding hay in a haystack.