1881 census has:
Onchan 27 Tynwald St PENDLEBURY James Head M M 46 General Agent born Bolton-Le-Moors England
Onchan 27 Tynwald St PENDLEBURY Elizabeth Wife M F 43 --- Bolton-Le-Moors England
Onchan 27 Tynwald St PENDLEBURY Matilda Martha Daur U F 19 --- Bolton-Le-Moors England
Onchan 27 Tynwald St PENDLEBURY John Albert Son - M 9 --- Bolton-Le-Moors England
Onchan 27 Tynwald St PENDLEBURY John Tuck Son - M 10 --- Bolton-Le-Moors England
Onchan 27 Tynwald St PENDLEBURY Jabez Son - M 7 --- Bolton-Le-Moors England
Onchan 27 Tynwald St PENDLEBURY Ester Ellen Daur - F 1 --- Douglas IoM
James is found as a picture framer in 1881 directory and as insurance agent in later dirs.
the birth place of youngest daughter would indicate arrived on island c.1879 - however note gap between Jabez and youngest daughter - query if remarriage? - also some children would appear to be missing as another large age gap between eldest daughter and son.
Jabez would indicate a Wesleyan Methodist to me (Jabez Bunting was 'Pope' c.1840-50)
Pendlebury is near Salford
There was reference in 1860's to a John Pendlebury of Manchester designing the covers for the Manx Society volumes but that is the earliest connection I can find