The Sight of Gandalf

[Essex]

The only time in ROTK (in the book) I can find that Gandalf has 'sight' is when he sees with second sight what takes place with the Witch King.

But Gandalf's face was grave and sad, and bidding Beregond and Pippin to take Faramir into the Houses of Healing, he went up on to the walls nearby; and there like a figure carven in white he stood in the new sun and looked out. And he beheld with the sight that was given to him all that had befallen; and when Éomer rode out from the forefront of his battle and stood beside those who lay upon the field, he sighed, and he cast his cloak about him again, and went from the walls.

And after trawling these boards for a number of months, I've finally realised why Gandalf asked for 3 eagles to take him to Mount Doom. He thought Gollum could still be with the Hobbits. So he did not have any 'sight' there either.

'Then come, and let your brother go with us, and some other of your folk who is most swift! For we have need of speed greater than any wind, outmatching the wings of the Nazgûl.'