“Thee” and “thou” in “The Lord of the Rings”

[Inziladun]

If Éowyn's use of the archaic forms is due to an emotional outbreak, what does that say for some of the other uses?

There are many examples in Denethor's final speech to Gandalf:

'With the left hand thus wouldst use me for a little while as a shield against Mordor, and with the right bring up this Ranger of the North to supplant me.
But I say to thee, Gandalf Mithrandir, I will not be thy tool!'

And later with the Mouth of Sauron:

'Then thou art the spokesman, old greybeard? Have we not heard of thee at whiles, and of thy wanderings, ever hatching plots and mischief at a safe distance? But this time thous has stuck out thy nose too far, Master Gandalf; and thou shalt see what comes to him who sets his foolish webs beneath the feet of Sauron the Great.

I'd always thought the use of the old forms by Denethor annd the Mouth to have been a result of the speakers' desire to lend their words extra authority at those moments.