Quando Denethor começou a usar o Palantir de Minas Tirith?

Bem, temos um limite superior óbvio de TA 2988 (dos Apêndices A e B):

2988 Finduilas dies young.

‘After [Finduilas'] death Denethor became more grim and silent than before, and would sit long alone in his tower deep in thought, foreseeing that the assault of Mordor would come in his time. It was afterwards believed that needing knowledge, but being proud, and trusting in his own strength of will, he dared to look in the palantír of the White Tower.

Temos um limite inferior, também do Apêndice A, de "antes de seus filhos chegarem à idade adulta":

‘In this way Denethor gained his great knowledge of things that passed in his realm, and far beyond his borders, at which men marvelled; but he bought the knowledge dearly, being aged before his time by his contest with the will of Sauron. Thus pride increased in Denethor together with despair, until he saw in all the deeds of that time only a single combat between the Lord of the White Tower and the Lord of the Barad-dûr, and mistrusted all others who resisted Sauron, unless they served himself alone.

‘So time drew on to the War of the Ring, and the sons of Denethor grew to manhood.

'when Estel was only twenty years of age, ... Elrond looked at him and was pleased, for he saw that he was fair and noble and was early come to manhood.

Assim, essa lacuna de dez anos é o caso mais provável para quando ele começou a usá-lo, desencadeada pela morte de sua esposa. Curiosamente, isso realmente o coloca mais cedo do que Saruman e sua armadilha:

c. 3000 Saruman dares to use the palantír of Orthanc, but becomes ensnared by Sauron, who has the Ithil Stone.

Mais é dito em Contos Inacabados sobre este assunto.

...when and why Denethor had dared to use the Stone was and remains a matter of conjecture.

His 'grimness' was first observable to others after his wife Finduilas died in 2988, but it seems fairly plain that he had at once turned to the Stone as soon as he came to power, having long studied the matter of the palantiri and the traditions regarding them and their use...

Do Palantiri, UT

Se isso for verdade, ele começou a usar o palantir em 2984 quando sucedeu seu pai.

O Apêndice A4 ("Gondor e os herdeiros de Anárion") conta essa história. A esposa de Denethor, Finduilas , morreu alguns anos tornando-se regente.

After her death Denethor became more grim and silent than before, and would sit long alone in his tower deep in thought, foreseeing that the assault of Mordor would come in his time.

Finduilas era de Dol Amroth em Belfalas , e não gostava da cidade murada de Minas Tirith e da proximidade da sombra de Mordor. Depois de sua morte, Denethor ficou ou permaneceu obcecado com a proximidade de Mordor. Isso, assim como os desenvolvimentos políticos e estratégicos, levaram-no a acreditar que um confronto direto com Mordor era iminente.

It was afterwards believed that needing knowledge, but being proud, and trusting in his own strength of will, he dared to look in the palantír of the White Tower.

O palantír não tinha sido usado desde a queda de Minas Ithil para Mordor, quase mil anos antes.

In this way Denethor gained his great knowledge of things that passed in his realm, and far beyond his borders, at which men marvelled; but he bought the knowledge dearly, being aged before his time by his contest with the will of Sauron. Thus pride increased in Denethor together with despair, until he saw in all the deeds of that time only a single combat between the Lord of the White Tower and the Lord of the Barad-dûr, and mistrusted all others who resisted Sauron, unless they served himself alone.

O apêndice não discute o que levou Denethor a usá-lo mais ou a desafiar diretamente Sauron. Para isso, só temos a especulação de Gandalf que você cita.