A question on Isildur

[Elf Girl]

In the movies, Elrond takes Isildur up to Mount Doom after Isildur cuts the Ring from Sauron's hand. Was it so in the books or did Isildur make his choice on the battlefield? Is there any evidence either way?

I need this for a piece of fanfiction on Isildur's thoughts as he tries to cast the ring into the fire.

[durin's bane]

Well, in the Council of Elrond, I don't remember Elrond mentioning that he tried to get Isildur to destroy the Ring, so I think Isildur had to decide for himself.

[Fat middle]

`Alas! yes,' said Elrond. `Isildur took it, as should not have been. It should have been cast then into Orodruin's fire nigh at hand where it was made. But few marked what Isildur did. He alone stood by his father in that last mortal contest; and by Gil-galad only CÃ*rdan stood, and I. But Isildur would not listen to our counsel.
' "This I will have as weregild for my father, and my brother," he said; and therefore whether we would or no, he took it to treasure it. But soon he was betrayed by it to his death...
It seems that the scene takes place in the battle field. Orodruin is "nigh at hand" but Isildur's attitude seems resolved from the very moment in which "Isildur took it, as should not have been".