Hi Shane,
You have been given a lot of information about the well-known Dumbells in the IOM (but not about your John’s father John Dumbell), the marriage and children of your John's probable Scottish mother, and (I assume) his half-brother's arrival to join him in NZ from Harry Leece. This shows that he was in touch with his mother and her children after her marriage, even though it looks as though he remained living with her Davidson parents and their other children.

Regarding his father who was named in the IGI as John Dumbell at your John's baptism it may help you to know that the IGI always lists bapts under the mother's surname, even though it was unlikely to have been written that way in the parish register. It was usual to write the entry (for example) as "John illegitimate son of ....".
In your case it was fortunate that both parents' names were given, but you can always recognise an illegitimate birth in the IGI because of their use of the mother's surname. However in the IOM at that time it was usual for the child to be known by the father's surname, even if his name wasn't given on the baptism record.

As information about his father is so scanty it would be a good idea to look up the copy of the Kirk Rushen parish register on film to see whether any other details about him were given in the actual record. You can see LDS films at local Family History Centres, worldwide (there are a lot in NZ). Look in the phone book under "Church of Jesus Christ of Latter-Day Saints" for their non-member opening hours. They charge a small fee to order the film to be delivered to them and it is yours for a month to read and photocopy on their film readers. They ring you when it comes in, and you book a reader for when it suits you. There are a lot of other records freely available in the centres as well, on film, fiche, CD, and online.
The film number to order to see John Dumbell's baptism record in Rushen is: 0106742 [Baptisms 1709-1841 Marriages 1708-1757 Burials 1712-1849.]
You would also be able to see family burials and Jane/Janet's marriage on 26 Nov.1831 in Rushen.

This Kirk Rushen film number can be seen on the IGI entry under Source Call No. at the bottom of the screen showing his bapt (at FamilySearch.org).

Many of John Dumbell's LEECE half-siblings are also in Rushen bapts on that film which would be interesting for you to see, in case there was further information about Jane/Janet, including:
Jane bapt 23 Dec 1832 Kirk Rushen
Elizabeth bapt 2 March 1834 Kirk Rushen
Catharine bapt 16 Aug 1835 Kirk Rushen
Thomas bapt 5 March 1837 Kirk Rushen
Alexr bapt 2 Dec 1838 Kirk Rushen
James bapt 27 Dec 1840 Kirk Rushen

I couldn't see his father John Dumbell in IOM burials, but there is a will in Brian Lawson's indexes which might be his, and if so would be why he has been so difficult to find, dying by 1832: DUMBELL, Jonathan, 1832, Braddan, Epis., No.1, LDS film no: 0106432. You could order that will film to photocopy the will at the same time as ordering the Rushen parish register. If he died so soon after his son's birth there is a good chance that his infant son would be mentioned, and Manx wills are often very informative and detailed.

I'll be interested to see what you find.

Sue