I suppose the biggest factor in determining undead eye coloration is ‘The Rule of Cool’. In other words, there probably isn’t much in the way of rhyme or reason as to why a Forsaken would usually have yellow eyes whereas a Darkfallen elf would have red eyes, meanwhile a random scourge ghoul could have yellow or red or green eyes. If it looks cool, it goes.
Death Knights are an exception due to being reanimated by the powers of the Lich King, but even that isn’t clear due to Bolvar himself having orange eyes… so is it The Helm of Domination itself that reanimates Death Knights? Or is it Frostmourne? Both? Neither? Who knows.
Bolvar was incinerated with Red Dragonfire and Fiery Undead always have Orange Eyes due to the Fire so even the Domination Magic couldn’t give Bolvar Blue Eyes until he drew upon a sufficient amount of Domination Magic to fight against Sylvanas.
Domination made Anduin’s Eyes go from Not-Glowing to Glowing Blue so yes Death Knights do have Blue Eyes due to Domination.
As for Red Eyes: Banshee-Form Sylvanas in Mawsworn Armor has Red Death Energies extending to her Shoulder Plates whereas they don’t outside Banshee-Form. Sira Moonwarden(another Darkfallen with Red Eyes) makes it clear she feels nothing but Rage(Wrath is one of the Sins harvested by Revendreth) and Ugliness.
Darkfallen are revived with their own Wrath and Dread it would seem due to Arthas’s desire to weaponize their Wrath as a Banshee-Wail.
Pure Pain would get Rainbow Black & White(the color of Mawsworn Death Magic which seems tied to Pain itself) Eyes I dare say.