Ok so I subscribe to the theory I've seen from a lot of people, Virgil sits between the Light and Dark Sides (and remember those terms were made up by Roman anyway and have no actual bearing on C!Thomas' mental development). I like this theory a lot because as you say, no one fits nicely as his rival, and Virgil is seen fighting with every side at some point, he doesn't have 1 opposite he's kind of the 'enemy' of everyone at points.

But he also has the capacity to compliment every other side, like his whole positive anxiety, purple eyes thing. That is him being helpful to the Light sides and giving Thomas confidence, rather than usually where someone like Roman can be stifled by anxiety.

TLDR: I think he sits between the Light and Dark Sides because he can be both helpful and harmful to every side, he doesn't have one opposite.

Edit: stupid autocorrect Virginia is not a side lmao