You know which one I mean.
Greavers wear masks with the symbol emblazoned on the front. Tier 2 Trojans have it carved into their shields. Aggressive red Tortodrones bear many on their shells, and subsequently every 5* Tortodrone Shield available has four. It's one of the parts of the Titan Gate icon. It's the distinct feature of Statues and Vortex bombs, with the same Eye being found on Kat Raiments. Seal Tags bear its visage.
And it's the unmistakable mark of the all-consuming Swarm.
How do all of these things relate to eachother?
For one, they all have esoteric origins:
•Greavers and Trojans are both Fiends, originating from an Underworld we've never seen ingame.
•Tortodrones are unique golems, with an origin unknown to even the Snipe-enthusiast Strangers.
•The Titan Gate was presumably created by Cradle's Architect, who knew exactly what they were doing when they made the icon.
•Statues bear the mark of Artifact (vortex) bombs, both of which have no clear origin.
•Kat Raiments are recreations of the armor of the cursed, long-dead Kat Tribe.
•The Dread Seal and the Faust/Avenger lines are stated as being weapons of ancient times.
But above all, the Eye is most prominent when used to reference the Swarm. Shadow Keys sport the icon, Shadow Lair stages are loosely referenced with the icon, Unknown Passages are identified by it, and in Dreams and Nightmares it's impossible not to see it, both as the entity at the Terminal and on every Arena gate encountered thereafter.
Is the Eye a mark of any one particular entity, force, or coalition?
Likely yes, as its usage marks the item or entity it's placed on as "incredibly ancient". Everything mentioned above is rooted in eldritch origins. It can be inferred that the sigil cane from one central location or race, countless ages ago.
If the Eye was only used to denote evil, it would not explain the existence of Tortodrones, Vortex artifacts, or Statues. However, if the assumption is that forces such as Undercorp. or the Swarm corrupted the sigil and thus its power for their own usage, it would explain both sides of the mark.
Thoughts?
First of all I think it's quite apparent based on all the ancient stuff we find that there was some sort of ancient civilization present on Cradle before the knights, the gremlins, and maybe even the fiends and Kats. It's possible that the Eye was the symbol of that entity, or a symbol used by that civilization for a certain purpose.
I think the more likely purpose of the Eye is as a warning, or a seal. It could be this world's universal symbol for "danger", a watchful Eye.
In context of everything else, I think it would make sense for the Fiends to be the oldest entity on Cradle. The Eye was ultimately derived from either them, or the Swarm.
The Tortodrones might have been created by the ancient entity mentioned earlier as guards for Cradle, and the Eyes on them represent the danger that the 'drones themselves present, and the danger of the areas they guard. The Eyes say "get out, it's not safe here".
The Titan Gate, created by the entity; that symbol might represent some sort of guardian (with a single watchful Eye) of the Clockworks related to the entity, and we just haven't seen that guardian yet.
Statues used in puzzles are almost always used to block off pathways in the Clockworks until their puzzle is solved, and the Eye warns you "this is dangerous".
The Vortex bombs were created using unknown and unstable theories and materials, so it would make sense for there to be a warning symbol on them. (Edit: as the creators of the bombs, the knights probably just thought it was thematically appropriate to put the Eye on something so mysterious and dangerous. Cheeky things.)
The Kat tribe was a tribe of warriors, and they may have included the sigil on their armor as a form of warning and intimidation.
The Dread Seal is...a seal, used to seal away something dangerous, and once again the Eye is there to warn you.
The Sealed Sword and its upgrades clearly hold great power, the 3-star Sealed Sword has dozens of presumably magical paper seals on it used to contain that power. With the 4-star upgrades, the seals have begun to be removed, and a large Eye sigil appears to caution you "there is great power sealed here, what you are doing is dangerous".
Also I think worth noting are the seals seen on the elemental Lumbers, presumably imbued with magical properties and used to prevent the Lumbers from being damaged by their environment.
And the Swarm. Either the Swarm was the ultimate origin of the Eye, and the use of the Eye as a symbol of danger was derived from it, or the Eye is used most prominently as a warning for the most prominent danger.