That made me look it up, and it turns out goat sucker birds predate the chupacabra by a couple thousand years. There was a myth that these birds drank goat milk (from the goat).

I remember reading the Dragonlance books in the 90s, and one character would talk about a cryptid called the "Goatsucker Bird" that was an amalgamation of those two things, and now I finally get that joke.