Perhaps at one point in time, like many identical twins pairs, Basch and Gabranth shared a special bond since both were depicted as knights in their younger days in one of Yoshida's illustrations shown in the ending credits. After the Archadian Empire invaded their homeland, Basch's decision to fled to Dalmasca and leaving behind Gabranth and their mother eventually led to the brothers to become estranged.
Throughout Final Fantasy XII, Gabranth acted hostile towards Basch, framing Basch for killing King Raminas and wishing death upon his brother. Basch was also seen being angry at Gabranth during his interrogation at Nalbina Dungeon (which was completely justifiable considering how Gabranth/Vayne framed and imprisoned him). When the party eventually arrived and fought with Gabranth at the top of Pharos, to the eventual battle on the Bahamut, it seemed that Gabranth was the one that had a problem with Basch, while Basch was trying to talk some sense into Gabranth, telling him to let go and stop blaming himself for his past mistakes and failures. Basch eventually coached Gabranth to reclaim his birth name, after the party defeated him on the Bahamut.
It was after the fight on the Bahamut that the brothers seemed to have reconciled. Gabranth fought alongside his brother and the rest of the protagonists during the fight with Vayne Novus (second form of Vayne). After being severely injured by Vayne while trying to land a fatal blow after the battle with Vayne Novus ended, Basch kneeled by his side to make sure Gabranth was not further harmed before chasing after Vayne with the rest of the group.
Basch was seen standing with Larsa next to a dying Gabranth on the Srahl after Vayne was finally defeated. As his final wish, Gabranth asked Basch to look after Larsa for him, entrusting his brother with the glimmer of hope for the peace of Ivalice he was finally able to see as he was dying. Perhaps Gabranth always had a lot of respect and trust for Basch before Landis fell and he was blinded by his anger towards Basch resulted from his own guilt.
A year after the main events in Final Fantasy XII, Basch was seen honoring his brother's dying wish and became "Judge Gabranth" while staying by Larsa's side.
Although on-screen interactions between Gabranth and Larsa were few and far between, in the one instance where both were on screen with speaking parts, Larsa, like his father, Emperor Gramis, showed a lot of trust and faith in Gabranth:
Vayne: Then let us look closer. Judge Gabranth! I would have you seek after the Lady Ashe... and adjudge whether she makes overtures of peace, or war. Yours shall be the eyes of the Empire.
Gabranth: And should I espy war, I am to put her to the sword. Is that your wish, Excellency?
Larsa: It will not come to that, I am sure. I have faith in her - faith in you both. On you, Gabranth, shall I wager all our fortunes.
On the Bahamut, as Gabranth was laying on the ground after being severely wounded by Vayne, Vayne sent his Sephiras (flying swords) hurling towards Gabranth and Basch (who was kneeling beside Gabranth), Larsa stood in front of the twins and defended them against his brother's wrath with his shard of manufactured nethicite.
As the party chased after Vayne, Larsa stood by Gabranth's side, sadden by the state the Judge was in. During the ending sequence, Larsa stood with Basch on the Strahl next to Gabranth and held his hand while he passed away peacefully with his lord and his brother by his side. From Gabranth’s dying words to Basch, it was clear that Gabranth see Larsa as his new master (he even asked Basch if Larsa was a good master on the Bahamut) and a symbol of hope for the future of Archadia.