"It's possible Kishi didn't intend anything by it, but in Hinduism/Buddhism there's an orthodox and an unorthodox approach to spirituality, which are known as the Right and Left Hand Paths [to Attainment], or Dakshinachara and Vamachara. There are a host of spiritual practices associated with both paths, and in both cases the associations apply pretty well to Naruto and Sasuke, or Ashura and Indra, Hashirama and Madara, etc."
To me Sasuke is and always will be a right handed person for the most part.
Chunin (Written) Exam episode (age 12/13) = he holds the pencil in his right hand = right handed
Kunai holster on his right leg = right handed (Remember the fake Naruto in the Forest of Death? Sasuke outed him because he noticed that the shinobi was left handed due to having his holster on his left leg)
When training with Itachi used a bow and arrow with his right hand pulling back the bow (age 7 max) = right handed
His sword (age 15 - 17) = nearly always held/used with his right hand = right handed
The only thing against this is the simple fact that he uses Chidori/reached out in Chapter 671 with his left. With the Chidori, it could mean he's left handed... Or that he prefers to take a risk/pierce his enemy with his weaker hand (the left) so that his stronger arm (the right) can be used if necessary.
The main reason why Sasuke is basically lefty (only) in terms of Chidori and such is that if he was right handed, then his powerful jutsu move would not meet exactly with Naruto's Rasengan when they need that awesome anime clash scene. From a side angle with two right handed people, someone's arm would be blocking the other and they both would be able to quite easily hit the other person's body at the same time without having the moves touch one another.
To me, it just doesn't make sense that someone throws, holds, and writes with their right hand more than their left and can be deemed a lefty out of the blue because of one or two cases. If Sasuke used his right hand as he usually would, then the drawings/anime scenes wouldn't look parallel and just wouldn't work.
So for story/artistic sake, he might be a lefty but come on... How can you write with your right hand and not be right handed? Or at least be called ambidextrous? I have nothing against left handed people (my best friend is a lefty and he's cool as hell) but logically, Sasuke is not purely lefthanded.
Though normally the left brain is the sun and the right brain the moon.. sol o mon the temple of solomon
But then again in japan the sun god is female (amaterasu) and the moon god is male(tsukuyomi) which normally is the other way around.