I think the clearest scripture, to me anyway, on how sin causes spiritual death is Romans 7:7-13.
I believe it is a mistake to place specific ages for things when the Scriptures do not. Basically, Paul states that once he understood the Law of Coveting, it then became the means of his spiritual death. So, the so-called "age of accountability" would seem to come once one is capable of understanding God's laws and then going against it.
So, what do we do about Numbers 14:29 here then? Is this God telling us that no one under the age of 20 is ever held accountable or even more to the point never spiritually dies and is in need of a Savior until the age of 20?
I don't think so. I think that Numbers 14, which chronicles the sin of the Children of Israel rebelling against God when they found out that taking back of the Promised Land wasn't going to be a walk in the part, is specific to that particular rebellion.
Back tracking from verse 29, we see in Numbers 14:3 the people crying out: Why did the Lord bring us here just to be killed? Our wives and little ones are going to become plunder... ahhhhhhgggghhhh, Let's go back to Egypt!!!!
God is ready to smite the lot of them and instead of Father Abraham make it Father Moses (this reaches back to the promises made to Abraham and also that Israel would become the line of promise) but Moses intercedes and God, making the point crystal clear that He did NOT lead the people to the Promised Land just so their "little ones" would be destroyed, placed the punishment for the rebellion on all who were old enough to serve as soldiers in the fight but acted like cowards instead.
To spin this out that this means that no one under the age of 20 is held accountable for sin is adding a lot more to the text than should be, in my opinion. 20 was the age of the fighting men of Israel, and I've always been taught that was so that young men could marry and have children prior to facing death in wars.
The Romans 7 passage seems much clearer as to when we become old enough to spiritually die.... It's when we are old enough to understand God's laws...but break them anyway.