It's not clear what it means when Saya and Diva's eyes glow. I've seen this being referred to as "chiropteran mode'. Saya's eyes glow in battle, in her Vietnam awakening and when she receives Hagi's blood to awaken in the first episode. Her personality changes and she is aware of what she needs to do and commands for a sword to be given and fights.
Diva's eyes glow frequently. They glow when she drains Joel's blood, and it looks like even after. When she wakes in the basement of Amschel's castle, her eyes glow when she sense Amschel approaching and again when she sees Solomon bleed out. Her eyes glow when she feeds on the human Karl. Her eyes glow when she drinks Riku's blood, when she targets Riku for assault, when she and Saya battle on the burning ship. Lastly, in the final battle. Her eyes glow when it looks like she is ready to fight.
Saya says in episode 30 that she is just like Diva, she kills innocent people. In the Vietnam war, Saya went berserk. Diva appears to do so as well. Do either of them have control? Saya remembers what she did.
When are the times Diva appears to be in a similar berserk mode? She killed the entire party in 1883. In episode 19, when she wakes, she kills the people who entered her container. When she is resting in the penthouse garden, there are scores in the ground, and broken tree branches, indicating that she had been violent.
Diva has demonstrated that she can use her strength without the glowing eyes. The glowing eyes might simply be a change in state of mind. Similar to excess testosterone affects personality, the glowing eyes are a sign of a battle-ready person.
