
not much spoiler
The golden hair and red eyes are symbolic of the imperial family since the founder of the empire had those characteristics. Kiolle is not Kishiar's and Keilusa's cousin (Kiolle is the adopted son of Keilusa the Emperor), but they are related because since they share those characteristics, they are all descendant of the fist emperor.

No hold on!
Kiolle de Diarca! Is the youngest son of Duke Diarca! I think the you mean Kachien when referring to the adopted son of Keilusa!!! Kachien’s mother had royal blood so duke Diarca took Kachien in when he was young to make him the crown prince so he could gain power!!! I think Kachien is also a relative of the Diarca family that’s why he could take him in and suggest him for the crown prince position! And yes Red eyes and golden hair are the characteristics of imperial family!

I believe it’s because the imperial family and the 4 ducal houses are descendants of the first emperor!
The first Emperor was born with the blood of the Sun God and was the greatest Swordmaster in history, while the first Empress was a powerful mage. They had five children; one became the next emperor, while the other four became the ancestors of the current Ducal houses of Tain, Diaca, Heren, and Apeto.
I remember someone saying that kiolle might be kishiar's cousin or smthg since him, kishiar and Emperor they all got blonde hair and red eyes and eye and hairs are very much correlated to family background in manhwas .