It's all speculation but it's mentioned by Ignis that Gilgamesh had been around for 2k years and he was a shield to a founder king.

Gilgamesh also glows red when warping similar to
Ardyn. (Kings share their powers like Noctis/Regis did)

And Gilgamesh might be immortal because of the curse placed on Ardyn? Would possibly explain why he still has those powers with Ardyn living.