No, I mean chapters 3-24 of Luke. (Not every single verse, obviously: I am just excluding chapters 1-2 in a general way from the main body.)
That is probably also true. Chapters 1-2 and chapters 3-24 probably hail from the same area, but neither used the other as it was being composed. They are independent.
I think the author of gLuke knew about Lk 1-2, because of "son of Zechariah" in Lk 1 and Lk 3.
What I am saying is that chapters 3-24 appear to be ignorant that they are cousins and that John actually recognized Jesus even in the womb. Luke 7.19, for example, comes as a bit of a surprise.
I do not see why Lk 3-24 should remind that John the Baptist and Jesus are cousins: That's done in Lk 1. Once is enough.
As for Lk 7:18-19, "John" has disciples, which is understandable for John the baptizer because of his great popularity. That "John" is not John the fisherman, one of the twelve, who was very unlikely to have disciples. Furthermore, John the fisherman is close to Jesus & would not need others to ask his questions. However, with John the baptizer in jail, intermediaries would be needed.
I do not see why Lk 7:18-19 should remind the readers/listeners that Jesus and John the baptizer are cousins. For me, that reminder would be a bit of a surprise because of unnecessary.
John is not named with a patronymic like that even in Luke 5.33, two full chapters after Luke 3, and with John the apostle intervening as another man with whom he could be confused! Introducing him afresh in 3.2 is simply unnecessary and strange.
So far, only two "John" are mentioned. John the fisherman is very unlikely to have disciples, but John the baptizer, because of his huge popularity, would have followers.
I think you expect the author of gLuke to be as accurate, precise and systematically consistent as, let's say, the scientist writing a paper on his discovery or a lawyer writing a pre-nuptial document. Well, gospel authors were not like this. You should know about that.
As for 3:2, I expressed myself already on that. I want to add, that the author of Lk 3:2 wanted to make sure that "John" was the same as the one in Lk 1. So, I do not think that reminder is unnecessary and strange.
Same tradition or area of influence. People probably knew John's patronymic and used it at will. It is the sort of information that would most naturally be readily available in a culture in which patronymics were the single most common means of identification.
After Lk 3, John, the son of Zacharias, would be known as the baptizer & a very popular preacher, and very likely to have followers, and therefore identified as such. No need to remind the readers he is a cousin of Jesus and/or son of Zecharias.
BTW, I do not see in the gospel, the author reminding the readers/listeners that Jesus is the son of Joseph, or that John the fisherman, who will become a member of the twelve, is the son of Zebedee.