One of those sections is found 6-1, a section devoted to Church Members. This section says,
The children of believers are, through the covenant and by right of birth, non-communing members of the church. Hence they are entitled to Baptism, and to the pastoral oversight, instruction and government of the church, with a view to their embracing Christ and this possessing personally benefits of the covenant.
I was reminded of the nuance here in a recent session meeting as we were picking apart some of the finer points of sacramentology in clarifying a pastoral issue. A few elders were claiming that non-communicant membership comes through baptism, while others were arguing (in line with the Book of Church Order) that a child's membership in the church is "by right of birth" primarily. The Book of Church Order settled this dispute for us quickly. It is the latter.
The point here is that children are members of the church through and because of their parents, a concept called "federal/covenantal headship." As Christ represents believers before the Father as their "head," so parents represent their children before the Father as their child's "head." Baptism is a gift and a grace children receive because of their birth-right, simply because God has chosen to use families as a vehicle of redemption. And it is the birth-right which makes them members of the church, not baptism itself. This is not to undermine or lessen the power of baptism, for in and through it we are further united to Christ in a myserious way, but only to say that when we speak of membership in the church for covenant children, they access it by their birth-right, not by baptism itself.