The seventh son has a connection with Jesus Christ in several ways.
Seven is said to be the number of spiritual perfection.
In the new testament Jesus is said to have six brothers and this is referenced several times.
In the book of Revelation 5:6 there is reference to many sevens all related to Jesus Christ.
The time of birth during a full moon may be the key element of a seventh son, Christ is said to have been crucified during a full moon at Passover.
I am a seventh son born on the 14th, my mother and father was also born on the 14th.