Not much is known or canonized about Oinodaemon so this is basically personal interpretation and that I have yet to see in any threads. I'm not a Galorion scholar but I'm tipping my hat in what this fifth horsemen may be from it's imagery, narrative throughlines, and the fact it's a daemon.
So first foremost, the daemons are beings of complete and utter annihilation. Secondly, it's tied to an eternal eclipse as being akin to an eye. Thirdly, is the most powerful amongst the horsemen, entailing it being a god of a calamity amongst a civilization and the world in general. Fourthly, that it's been hidden away to be forgotten by the realms.
I don't know how to not shorthand it immediately, so I'm just going to. I think the Bound Prince is of the Forgotten or forgetting. The last calamity to beset all things and all people.
Daemons are the only fiends amongst the three that would be direct agents of lost history and purposeful destruction of knowledge, or in other words the past. Demons main drive is to corrupt and cause widespread discord and devils seek to rule over all things, neither are of absolute destruction. (Obviously, both could perturb lore, scripture, knowledge, and historical accounts into lies, but they would be the indirect effects of their actual goals)
His imagery is that of an eye. It's a reach, but eyes are symbols tied to knowledge. I know it isn't a super compelling piece of supporting evidence as big eye in the sky is typical shorthand in fantasy for scary big god but this is specially for him in the setting and eyes being 'consumers of knowledge' I think it's fair to point out.
History and knowledge is something that can never be recovered once lost. A society can recover from war, famine, and plague. Even in death a society or person can live on to inspire new, great things, but there's no recovering from total erasure in knowledge.
The fourth one is an obvious tie for my thesis to what it is.
Fifth reason is that it's just cool. Daemons are fairly flat in how they're portrayed in lore in the goal of eating souls and also the rest of the world, which is insidious but isn't understandable compared to demons who seek true discordia through base instincts and desires and devils who desire everyone to be under their heel. So the addition that they are purposefully destroying knowledge and culture, thus giving rise of the importance of libraries and museums in lore, is something of a breath of fresh air into a fiendish race that is a bit simple.
(Also none of the fiends are stated to target knowledge, and destroying knowledge being obviously evil, daemons would be the best candidate for such an activity amongst the fiends)