I think you are
yin and yang:
In my enemy is my friend
In my friend is my enemy
Seemingly contrary forces can be interlinked, such as good and bad or light and dark.
I exist because he does
But he exists from where I don't
The concept of bad can only exist if good does, and vice-versa, and where there is not bad, there can be good. (Same applies to other apparently opposite forces.)
Round and round we go again
Each placed in the other's domain
As on the traditional symbol, the swirls follow each other.
But most places we are seen
We are seen as part of the same dream
Sometimes there's a fine line between the two, or none at all.
Where 1 is 2 and in that 2 are 2 more
The one symbol has two swirly shapes in, each containing one small circle.
My purpose is to show
You can't have one without the other, forever more!
The symbol represents the concept of duality, which could be called timeless.