In studying the effects of alcohol on the human brain, we know that the back lobes control basic motor functions that include walking, talking, and vision. These develop first in a person from birth thru childhood. The frontal lobes deal with higher reasoning, critical thinking, and decision-making capabilities. But the frontal lobes aren’t fully developed until the age 25 or so. Seeing as the frontal lobes are what would help formulate what a person believes (or don’t believe), wouldn’t it be a safe assumption that the age of accountability is actually then, rather than the traditional belief of 13-18?
There is no clear Biblical direction on what God sees as the age of accountability. There is only Hebrew tradition, which places it at 12 for girls and 13 for boys. Of course one would suppose that when the tradition was established it would have been after consultation with the Lord. According to my understanding of Romans 7:9 it was in place when Paul was growing up, which would have been during Old Covenant times.
The ceremony held for Jewish youth is called Bat Mitzvah (daughter of the commandment) for girls or Bar Mitzhah (son of the commandment) for boys. They are looked upon as adults following that ceremony and are expected to uphold the Jewish commandments and laws.
Personally, I encourage parents to speak with their children about the need to be saved well before this time, and would never suggest delaying beyond it, especially with the end of the age so near.