light-o

He just hung Goronui up there, on the wall! Hah... He never changes...

Light proceeds to find out the connection between Yotsuba and Kira's killings

Namikawa speaking about the police focusing on Kira's criminal killing history instead of the business men. He claimed whoever found the connection between Yotsuba and Kira must be a god.

On the topic of Light and Misa's relationship after L dies.

A part of me finds it funny how the two people in the entire cast of death note who would be the least likely to admit that they are miserable with their lives come to live together.

It's sad, yes, but it's also funny in the way sad things are sometimes.

Like you have Light, who is miserable because he has doomed himself to a life of boredom once again after killing L. Except this time it's worse because now he knows what it's like to not be in ennui. Now he knows what it's like to have someone that thinks on the same wavelength as him and to face off against them and he will never be able to experience that high ever again because the one who gave him that high is dead. L's grave has been dug - his body buried. He will never ever wake up again to play another game with Light.

On the other hand you have Misa who has not only sacrificed what is like 75% of her life (not that I think that she actually wanted that long of a life) but also the one being since her parents died that loved her dearly. Rem is dead and she has been sacrificed by Misa for the love of a man that is incapable of loving her. She spends her time desperately trying to find traces of love in her life with Light but she can't find them no matter how hard she tries and self-delusion can only take her so far. As a solution she tries to seduce Light which - do I even have to explain how poorly that works? Plus Misa's misogyny internal or otherwise and her self-destructive tendency to recklessly destroy her platonic relationships with others makes it hard for me to imagine her having a deep relationship with anyone in her life. So once again in her life, Misa is alone and loveless which is probably something she considers to be a fate worse than death.

But will these two part way and try to find joy in their lives?

No. No they will not.