“Are there any other details about the eyes? Is there anything specific to when a human uses them? I assume I wouldn’t be able to see my own lifespan.” Akihito attempted to get as much information as he possibly could about the functionality of the eyes before he agreed to anything concerning how long he lived. He could see a practical and defensive use for the Death Note and when combined with the eyes it would appear that he could kill anyone just by looking at them and writing their name down. Not that he would kill willy-nilly - more that he could use it if ever involved in a bank robbery, for instance. 

“Humans who possess the eyes of a shinigami have certain restrictions, but not many. They cannot see their own lifespan above their head or above the head of anyone else who owns a Death Note. Though, the probability of that is unlikely.” Midora allowed the boy some time to consider the offer, he didn’t need it.

“I’ll do it. As far as I’m concerned, within my lifetime, the secret to immortality could be discovered, however unlikely. I don’t know how long I will live, if I am destined to die tomorrow it’s worth it and if I’m destined to die one-hundred years from now, it is still worth it because I do not know. It also assures me that there is no way that fate can be cheated, I am destined to die and when I do, I will. So, yes, I’ll take it.” 

“Are you certain? There will be no going back once the deal has been made.”

Akihito looked directly into the eyes of the god of death before him, “Korera wa jōdante iru hito no me no yō ni miemasu ka?” 

“A fair point…”

[i]Japanese translation: Do these look like the eyes of someone who is joking?[/i]