Nerve element of brachial arch are developed from
Ref. Gray’s anatomy.  41st edition. Page. 449.
Topic, Subtopic – Brachial arch, embryology
Branchial or pharyngeal arches are masses of mesoderm covered by ectoderm and lined by endoderm. Within these masses, muscular and skeletal components develop, as well as aortic arches and nerve networks. The arches are separated by grooves, visible on the surface of the embryo as pharyngeal clefts and in the interior as the pharyngeal pouches

In the human embryo, the arches are first seen during the 4th week of development.
They appear as a series of outpouchings of mesoderm on both sides of developing pharynx.

The neural crest are bilaterally paired strips of cells arising in the ectoderm at the margins of the neural tube. These cells migrate to many different locations and differentiate into many cell types within the embryo.
Ectoderm
Neural crest cells
Endoderm
Mesoderm