Santa Fe's captain yakked on the radio and he was overheard. The British did not find him. He gave away his position and they stumbled across him..
However Santa Fe was found she was attacked and run aground at Sth Georgia a week before Invincible reached the TEZ, and even then the TEZ is 800 miles from Santa Fe's last position. She got nowhere near the Invincible, let alone conduct an attack that failed due to faulty torpedos.
HMS Brilliant was the RN goalkeeper for HMS Invincible. In the USN parlance, she was the threat axis missile trap and ASW bodyguard on that same threat axis. San Luis was attempting to get past her to get Invincible.
The Wiki talk you reference says Brilliant was "Detached on 1 May to search in the suspected position of San Luis off Stanley", thus she was not near the Invincible during the sub hunt. San Luis did not get into an attack position against the Invincible, let alone fire torpedos at her that failed because they were faulty.
In fact diesel-electric submarines are not very good at hunting carriers in the open sea, mainly because the carriers are moving along at a sustained 20kts or more and speeding up to 30kts while the sub is trolling along at 4kts submerged and snorting at 6kts. Maybe the sub can put itself in a position where the carrier heads toward it, but of course that's where the ASW escorts are because they know where the carrier is going and if the sub speeds up it will make itself obvious and be attacked while the carrier veers away.