The full 1861 Maughold census entry has:
3 16 Dhoon
John WADE Head MAR 22 b.German
Ann WADE Wife MAR 23 Maughold
John WADE Son 1 Maughold
Ellin WADE Daughter 0 Maughold

John James Wade bapt 4 Sept 1859 Lonan, son of John Bell Wade & Anne Corkill?
Eleanor Jane Wade bapt 3 March 1861 Dhoon Christ Church daur of John Wade & Anne Corkill.

Other bapts in Maughold with parents John Wade & Anne Corkill:
William Henry son of John Wade & Ann Corkill bapt Dhoon Church 5 Apr 1863
Evan Christian son of John Wade & Ann Corkill bapt Dhoon Church 12 Feb 1865
Robert Edward son of John Wade & Isabella Ann Corkill bapt Dhoon Church 5 May 1867
Ann Maria daur of John Wade & Isabella Ann Corkill bapt Dhoon Church 29 Nov 1868
Catharine Margaret daur of John Wade & Ann Isabella Corkill bapt Dhoon Church 9 Oct 1870.

In the 1881 census they are in Lonan [FamilySearch]:
John WADE Head W Male 42 German, Isle of Man, England Lead Miner
Edward WADE Son Male 14 Maughold, Isle of Man, England Lead Washer
Fredrick A. WADE Son Male 5 Lonan, Isle of Man, England Scholar
Ellenor J. WADE Dau U Female 20 Maughold, Isle of Man, England Housekeeper
Ann M. WADE Dau Female 12 Maughold, Isle of Man, England Scholar
Margret WADE Dau Female 10 Maughold, Isle of Man, England Scholar
Source Information: Dwelling Kingley 12
Census Place Lonan, Isle of Man
Family History Library Film 1342346
Public Records Office Reference RG11
Piece / Folio 5601 / 84 Page Number 8

There is an extracted record in the IGI for the marriage of John Wade & Bell Anne Corkill 29 Jan.1859 Lonan.
This should confirm his father's name and occupation.

Sue