Witch King

[Essex]

So the WK leaves Gandalf behind:

The darkness was breaking too soon, before the date that his Master had set for it: fortune had betrayed him for the moment, and the world had turned against him; victory was slipping from his grasp even as he stretched out his hand to seize it. But his arm was long. He was still in command, wielding great powers. King, Ringwraith, Lord of the Nazgûl, he had many weapons. He left the Gate and vanished.

Tolkien vaguely describes the WK moving to his Fell Beast, inasmuch as the text in bold below.

Upon it sat a shape, black-mantled, huge and threatening. A crown of steel he bore, but between rim and robe naught was there to see, save only a deadly gleam of eyes: the Lord of the Nazgûl. To the air he had returned, summoning his steed ere the darkness failed, and now he was come again, bringing ruin, turning hope to despair, and victory to death

before the darkness failed - therefore STRAIGHT after the cock had crowed, because Dawn was arriving, and the darkness was 'failing'.
(of course you can read 'darkness has failed' as NOTHING to do with the Dawn of course, but then that's one of the reasons we have so many 'arguments' over what Tolkien's point was in certain parts of the book.......)