Answer:
First, we have to understand that the concept of "spiritual" is different from culture to culture and especially, time after time. Anyway, the "spiritual quest" in Gilgamesh can be sum up into three stages:
Gilgamesh's quest involve answer these questions, and find a way to explain himself. That's why we can describe his journey as a spiritual quest. The journey he undertakes, if separated into the Stages of Soul, then we have:
Maybe the better answer to the message of this tale is that life is precious, and you must live plenty. You see, Gilgamesh was a futile and lazy king, but also vicious and violent. He was wasting his life, so he finally realizes it's importance, but also learn that loneliness is painful. He never care about anyone but him. When Enkidu dies, he understands the value of a friend.
Explanation:
The Epic of Gilgamesh is a classic tale of return carrying a message that was obtained through terrible grief and struggle. But also, a personal point of view of the human soul.