Wiping the neck during Wudhu is not from the Sunnah, rather it is an innovation.
[al-Badar al-Muneer v. 2 p. 221]
There is nothing authentically reported from the Prophet regarding wiping ones neck during wudhu.
[Zaad al-Maad v. 1 p. 195]
Shaikh Ibn Baaz:
Wiping ones neck is not prescribed, only the head and ears are to be wiped during wudhu, as established in the Quraan and the Sunnah.
[Majmoo fataawa v. 10 p. 102]
I do not see it permissible to wipe ones neck during wudhu, except that a daleel is provided that is authentic, showing its legislation and since there is none it should not be done.
[Tamaam al-Minnah p. 98]