I can't find anywhere in the book where it states which side you use when you are in neutral stance. The way I see it you must inevitably end up being in Neutral stance from time to time when in combat. You start in it and it says nowhere that you must move to either conservative or reckless stance. and what if you wish to change from one to the other during a fight? you will cross the neutral stance.
So far i'm just asuming you use the conservative side without being able to convert stance dice.