I think you all are just overthinking things. Just look at the issue through the lens of cognitive dissonance and self-image.
Neutral recognizes that Good is "better" than they are. They would like to be Good, but can't hack it because they are too greedy, jealous, spiteful, wrathful, or whatever. However, they need to feel morally superior to someone, so they can't let Evil die out. At the same time, they don't want to live in a world where Evil has the upper hand (who would?), so they can't let them win, either.
Thus, they join forces with Good when Evil gets too strong, and quietly help Evil to survive when Good starts winning. To make themselves feel better, they dress it up in high-sounding language like "standing up for the underdog", or "helping the weak", or "maintaining the Balance".
Done.