Simply put - this is a Hollywood-ism specific to Disney and the Pirates of the Caribbean franchise. There's no basis for pirate cosmetics of any kind. Johnny Depp as Jack Sparrow is pretty much the origins of it. Nothing to do with historical pirates.

EDIT: The closest thing you'll get is one account where pirates were mocking the upper class and coated themselves in wig powder and acted all posh for others to laugh at.

This originated with the Pirates of the Caribbean. There's a feature on the 2006 DVD called 'Jack's Eye Makeup' in which Johnny Depp talks about originating the idea himself – he is wearing kohl around his eyes, which he says he chose after studying various nomadic tribes that he said used it to resist the harsh glare of the sun.