Some animals with an appaloosa white pattern have tails that tend to grow very sparsely and the hair won’t grow very long past the end of the tail bone. This isn’t a defining factor, but simply a genetic trait that can display (on both appaloosas and Curly breeds) and generally affects the mane too.
For some the rat tail is a sign of ‘old blood’ or ‘foundation type’ and considered true appaloosa genetics. Others speculate that this trait was bred for by Native Americans to keep it from getting caught on things while hunting. This is just myth, spotting patterns originated outside of the American continents and are depicted in ancient art from around the globe. Today breeders are trying to create those lovely spotted coats with luxurious mane and tail hair and having some success. Perhaps the rat tail trait is not genetically connected to the white pattern itself.