First of all - the Greens have never been a left wing party in the traditional sense. They are not a broad-based movement based on and from working class people.
The Greens are more a middle class party of the age of identity politics. In other words, people today seem more to identify with a racial or social group than they do with a broad economic class. hence, for some people being a biggie is more important than being a Maori, or being a Maori is more important than being a member of the working class. Hence, gender (two leaders for gender balance), race, and sexuality all play a big part in Green politics alongside those of the environmental movement who founded first the Values party then the Greens.
Of course, identity politics now dominates new Zealand politics. Anyone looking at the media spin around the National government and it's cheerleaders in the editorial team at the herald can see this. The clear message is all about identity. The wicked witch is dead, that the rule of academics, lesbians, gays and P.C. brigade is dead and white, aspitational middle class (who in in struggle street doesn't want a pink McMansion in Omaha?) heterosexual men are back in charge.
So the idea that the Greens will "go to the left" is a complete nonsense. unlike Labour they don't have a traditional class based left wing in their party to challenge the practitioners of identity politics. The Greens have no empathy for and are largely distainful of the working class. Sometimes (perhaps even more often than not) their policies align with the left, but it isn't left wing philosophy that drives them.
Which also says to me that if it was properly organised, under MMP we could probably get a biggie party candidate elected to Parliament...