Is this boy the son of Emma Fearn aka Frost/Fern/Reader? (James Jellyman owned the house she lived in, according to one newspaper report).
How sure are you that the electoral roll entries and the 1913 newspaper record are your Arthur? The 1913 record indicates that this particular Arthur Fearn had only arrived in Blenheim recently "with a circus".
http://www.rootschat.com/links/0utl/ &
http://www.rootschat.com/links/0utm/ are interesting, the first because it shows some link between Jellyman and Fearn in terms of property inheritence (but who was Mrs Jones - perhaps Emma Reader who m. William Jones in 1886?), the second shows both he and his mother using "Fearn" in 1904.
ETA: Think Mrs Jones may be the mother of Arthur and various other kids who married William Jones - she seems to have taken on the name Helma Jones which appears on her probate in 1907. Her sister, Evelyn Ann Reynolds wife of Alexander, states that she was generally known as "Emma" on the probate records - Arthur Fearn is also listed as an executor, stating that he is the son of Helma/Emma, who was the widow of William Jones but at the time of his birth was the wife of Thomas Fearn from Motueka, a bootmaker.
It seems the entirety of Emma's estate was not properly disposed of. Documents from 1939 in the file state that Evelyn Annie Ridgeway (late Reynolds) had died in 1931, and Arthur Fearn had lived in Blenheim until about 1909 but then left, and that he had not been seen by friends/relatives beyond 1914. Newspaper advertisments had been placed to find "Arthur Fearn or Jones, son or step-son of Elma, Alma, Emma, or Helma Jones", without any luck. (these can be seen on familysearch.org/ )