On this island, a third type of person can say anything at all

You can't — and that's the point. A knight could never say it (it would be a lie). A knave could never say it either (it would be true, which a knave can't say). So the speaker must be a normal — the one case where adding an unpredictable third category actually lets you deduce something, by elimination, that pure knights and knaves alone couldn't tell you. Raymond Smullyan introduced 'normals' as a twist on his classic knights-and-knaves format to show how far pure logic can reach even when one source is entirely unreliable.