Gau and Sabin's relationship is a weird one. Sabin went from being annoyed by Gau, to respecting him, and then actually caring about him. Gau's story is actually really sad, but Sabin makes it a little better.
Gau was a wild child, living loose in the Veldt. He wore monster skins, didn't speak well, and had no idea how to act around people. Sabin and Cyan ran across him when they washed up on the Veldt. Although they were unconscious and didn't know it, Gau was shocked and worried when he saw Sabin laying there unconscious on the beach (and probably Cyan too), and went to check him out, probably to see if he was okay. Sabin woke up, and naturally he was curious, so he asked Gau who he was. At that, Gau ran away.
The player takes control here. To obtain Gau, you'll need to go to the nearby town Mobilz and buy some Dried Meat. Walk around the Veldt and fight monsters that pop up. After one of the battles, Gau will appear mumbling something about how hungry he is. Have Cyan or Sabin feed him the Dried Meat, and you'll unlock a scene in which Gau joins your party.
Gau was not like people Sabin or Cyan were used to seeing. He was a little hyper, and a little too immature for their liking. Sabin is the one that stood up to Gau as an older, more mature person, and tried to get him to calm down. I'm not sure if that was a mistake exactly, but I think it's definitely what triggered Gau and Sabin's relationship. Gau saw that Sabin was getting annoyed by him, so he made it a point to annoy Sabin. He even came up with a nickname, calling Sabin Mr. Thou. It's funny that he attached it to Sabin since Cyan was the one who regularly used the word, but Sabin got sufficiently annoyed by it, so Gau continued using it.
I think Gau fed off that reaction from Sabin. He wanted him to get annoyed. Sabin's downfall there is that he couldn't just ignore Gau like Cyan could. He had to pick on him back.
You're a regular munchkin!
And thus began the love/hate feeling Sabin had for Gau. It was Cyan's idea for Gau to join their party, and even though Sabin questioned it at first, I believe Gau really began to grow on Sabin. He took Gau and Cyan back to his friends at the Returners where both became valuable members of the group.
Later on in the game, you can unlock an important Gau and Sabin scene if you have them both in your party and come across a man's house near the Veldt. Sabin believes the man in the house is Gau's father, and he tells Gau it's important for him to tell that man he's his son. Sabin said it was a once in a lifetime event though, and wanted to take Gau to Jidoor and get him dressed up.
In this scene we learn that Sabin had been spending some time with Gau, helping him fit in with society.
No, Gau! How many times do I have to tell you not to eat with your fingers?
To me it seemed that Sabin had sort of taken on a big brother role with Gau, and was watching out for him, sort of like Edgar had watched out for Sabin. I think Sabin really looked up to Edgar for all that he had done for him, and aspired to be like him in that way. I think that's why he took Gau under his wing. Gau definitely needed a big brother figure, and Sabin fit the role perfectly. I think he helped make Gau a better person.
Listen, Gau. You're going to go in there now and show your father what a fine young man you've become!
After Gau was dressed up the group went inside the house where Sabin confronted the man, asking him if he had a son. The man denied ever having a son but said that he did have a dream where he took a demon boy out to the Veldt and left him. He said when he looked back he saw a hideous monster and ran away, never looking back again.
Sabin grew angry and wanted to fight the man, but more than that, he grew sad for Gau. Sabin truly cared about Gau at this point, and the typical big brother reaction in him was to grow mad. Outside he apologized to Gau, but Gau said he was happy just knowing his father was alive.
Even though the scene ends there, I think Gau losing his father, although in a less traditional sense, probably made him grow closer to Sabin. Sabin had lost his father in a different way, but I think that might have helped them connect. Like Sabin and Edgar, Gau had no family in the typical sense of the word, but as long as Sabin was around Gau would always have him.