Well I think Yuta wants Seunghyun to sign the contract because like he said if Kujo were to tell him to kill him, he would have to do it. And Yuta said he has nothing to look forward to life so he really doesn’t mind dying. This was his plan from the start. And from what we’ve seen in past chapters, it’s seems like the Kujo clan don’t really like having Yuta as the clan leader. They’re most likely going to replace him w the stepson or somebody else.

Okay so I reread the last few chapter and basically Seunghyun thought he was doing the right thing and keeping his promise to Yuta (to bring him out of the Golden Pavilion). He didn’t exactly keep his promise because he himself did not go back for him, he hired someone to do it. However, the guy that he hired to do the job ended up betraying him bc he was paid 10x more by the Kujo clan. The old guy that Yuta ended up marrying was the one who ordered it. And Yuta stayed as a prostitute there before marrying the guy. He (the guy that was hired) was told to give Seunghyun the tie he gave Yuta as proof that he was now safe and freed from the Golden Pavilion. The saddest part tho is what Yuta pointed out in the last chapter. Knowing how meticulous Seunhyun is as someone who rose up the ranks to become a Yakuza boss, didn’t even bother to look for Yuta ever again and failed him. The fact that he did such a lousy job of choosing a random who easily betrayed him, to free Yuta just shows how much he really cared for him. That’s how Yuta sees it and honestly I don’t blame him. In his eyes the one person who made him look forward to life, didn’t even care to do that much for him. And he broke their promise.
I want to also point out what Seunghyun said this chapter: “IT'S NOT THAT I DIDN'T KNOW WHAT IT MEANT TO LONG FOR SOMETHING. I JUST RAN BECAUSE I WAS AFRAID OF LOSING IT. ARROGANT ENOUGH TO BELIEVE NOTHING COULD EVER SHAKE ME. BACK THEN, WITH HYUNG TOO... AND YOU... THE FUNNY THING IS, THE MORE TIME PASSES
WITHOUT YOU, THE CLEARER YOU BECOME. EVEN AS I WATCHED YOU GETTING HURT,
I STILL CHOSE MYSELF UNTIL THE VERY END. FROM THE VERY BEGINNING.” I assumed Seunghyun didn’t even know he had feelings for his hyung bcuz he acted appalled when Yuta mentioned that it was obvious he had a crush on him in I think ch 3? However he was just burying his feelings bcuz he didn’t want to loose him or ruin their relationship. He’s doing the same thing but w Yuta, but this time, his pride was the main reason why he couldn’t accept his feelings, and in doing so hurt Yuta even more than he already did when he didn’t go back to look for him and broke his promise.