Oddly enough, on my father's side they seem to have followed the naming tradition above fairly consistently, however, my mother's family seem to have reversed the sequence in terms of mother and father. I have many instances on that side of first son named for mother's father, second son father's father, first daughter father's mother and second daughter mother's mother. It happens often enough it can't possibly be just an occasional missing first child.
In very large families, the tradition could also extend to father and mother's grandparents, siblings, etc
I would add one proviso, which is to add "surviving" child. I would personally say a much more definite indication of a child being named after a parent, grand parent or even great grand parent is when several children are given the same name after the elder ones die in infancy. (eg if a first son were named James after the father's father, and that James died after just 4 months say, the second son would often also be named James, not named after the mother's father.)
The tradition was sufficiently strong that where a family had several daughters and no sons, the third or fourth daughter would often be named for the male grandparents - hence Williamina, Georgina etc)
