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He will say "My nose will grow now!", then it won't grow. Then once he realizes he lied, it will grow. How fast after he says it depends on what his perception of now is. Might be Instantly, a second delay, or a couple seconds delay.

if (nose = grow) when lying, and (nose = not grow) when truthful
by him saying that, his nose would not grow until it did not grow,
then it would become a lie and it would grow...

Case 1: Pinocchio is telling the truth (he knows that his nose will grow). Then his nose will grow. There's no stipulation that Pinocchio's nose grows only when he tells a lie, so this is quite possible. If that stipulation is in place, then Pinocchio's nose will not grow, contradiction.

Case 2: Pinocchio doesn't know whether or not his nose will grow, but this doesn't count as a lie. Then his nose will not grow (or it might grow for no reason at all; see Case 1).

Case 3: Pinocchio doesn't know whether or not his nose will grow, and this counts as a lie. Then his nose will grow.

Case 4: Pinocchio knows that his nose will not grow. Then his nose will grow, contradiction.

It's fun to think about it. I'm a mathematician and at my first year at school I got used to things like this.

If we concentrate on the statement itself and the context (we don't care, by now, if it's true or not): Don't you think it could be wired to see Pinocchio saying this an waiting to see whether his nose actually grows or not.

¿Do wood noses know anything about logic?

his nose will still be short

He was the son of a bootmaker, but one day the bootmaker failed, so he died before he could either tell the truth or lie.

If YOU believe it, it's not a lie. Example:

Ask any Christian if God exists. (p)erception = (R)eality