When did the Portuguese decide to extend their West African exploration to finding a sea passage to India?

It is possible that some Portuguese explorers had at least vague hopes of reaching India by sea all along. From the book Foundations of the Portuguese Empire, 1415-1580 (Diffie and Winius, 1977):

The birth of the idea that Europeans could get around Africa to reach the East cannot be traced to any precise date. The first to make the attempt were the Genoese. The difficulties of such a voyage did not necessarily seem in surmountable to the sailors of that time, given their misconception of the shape of Africa and the East as may be seen by looking at the maps available to them. [...] In May 1291 the Vivaldi brothers, Ugolino and Vadino, left Genoa "volentes ire in Levante ad partes indiarum" (desiring to go to the East, to the regions of the Indies). That they judged their task to be difficult can be seen in their preparation for a ten-year trip and their agreement to pay their backers half the profits (p.24-25)

The same source further explains in extensive detail how early Portuguese explorers benefited from contacts with Genoese and their knowledge.

However, I can't find any explicit mention of a Portuguese intent to reach India by sea until King João II sent Diogo Cão to try in 1482 (source, p. 150).

gktsck answer shows that the general intent to reach India was already there. But to understand how the general intent become a tangible aim, note that the path to India did not go through today's Ivory Coast, Nigeria, or Fernando Po. It went though Brazil, due to the direction of maritime currents.

What you have to look for is "When the Southern Atlantic "Volta do Mar" was discovered and mapped?'

... in the South Atlantic with the exception that the South Atlantic gyre circulates counterclockwise. As India-bound Portuguese explorers and traders crossed the equator with the intention of passing the entire western coast of Africa, their voyages took them far to the West (in the vicinity of Brazil.)

Before mapping the Southern Atlantic currents, "is it possible to go to India?" was just looking to a world map and wondering if there is some way - even the ancients could to that. After mapping the currents, they actually knew how to go south, and, instead of sending a few exploring ships in secret, they could risk a larger fleet (Vasco da Gama had 4 ships) to actually make history.

I doubt you will find an exact answer due to the secrecy imposed in the time and the loss of relevant secret documents from Portuguese archives through the centuries (*).

Even today people debate if Brazil was discovered before Cabral. A possibility is that they discovered and used the Volta do Mar to go to South Africa and India, and afterwards Cabral by chance went a little further west and found Brazil. (the official history).

Another possibility is that previous voyages had found signs that some land was nearby, and then Cabral used his voyage to India to purposely go further west and find the new land. Or, that they already knew Brazil was there and Cabral just claimed it publicly.

What is apparent is that they never stopped trying. We can assume that when they were in West Africa, Cape Verde, etc, they were also mapping Atlantic currents. Columbus voyage also depended on such knowledge and how he got that knowledge is also subject to debate today (he departed from Canarias).

(*) I was reading more and it appears "many secret documents were lost in a fire" is a Brazilian over-simplified historical legend which appears in popular sources and may refer to 1755. The Portuguese archives lost documents due to various events such as place changes, wars, and the 1755 earthquake. In 1755 the tower collapsed, but documents were recovered from the rubble.

I think there are serious problems with this question. Yet, I've decided to draft an answer, though not as detailed as I did to the related question here. The real problem here lies in defining what is a "decision to go to India".

My linked answer describes Portuguese knowledge of the Earth in the 15th century. Hence, it is likely that Dom Henrique thought from the very start that Africa was circumnavigable. However, that the continent was circumnavigable did not mean that it would be possible (unknown dangers, boiling ocean, sea monsters, etc).

Another option would be to consider the time after the Cape of Storms (Cabo das Tormentas) was rounded in 1488 and renamed into the Cape of Good Hope (Cabo da Boa Esperança)—though that future was still uncertain and that is why it was renamed by João II.

Especially with hindsight, it is easy to see all the previous steps that the Portuguese had made as one unending conquest of the unknown. It should be understood, however, that this was a process led by very few men, and that is why those leaders, Dom Henrique and King João II, are so important.

However, I decided that the most significant date was when Christendom was given the news that Portugal would be the owner of the trade of Africa and India: January 8, 1454 when Nicholas II published Romanus Pontifex. This was the real signal that Portugal had a goal, even if two decades would pass from the death of Dom Henrique with minimal progress (because there was no national leader for the program of explorations).

Romanus Pontifex's effect is described by Bradford in 'A Wind from the North':

The belief that before very long the Portuguese would manage to round the continent was strengthened by a bull of Pope Nicholas V in 1454, in which he granted Prince Henry the monopoly of all exploration as far east as India.