In those messages I wrote that to get any further you need to look at a number of films, either through LDS Family History Centres, or in the library at the Manx Museum.

I wrote:
Because it was noted in their marriage record that Philip Quayle came from Ballaugh, the most likely bapt for him was in Ballaugh on 2 Sept. 1770, son of William Quayle & Margaret Cowley. This date fits his age in the censuses and his burial.
So I'd try to confirm that by looking at several Quayle Ballaugh wills to see whether he is mentioned as a son "of Maughold", or whether his wife or children are mentioned.
e.g.
QUAYLE, William 1814 Bal Epis, 1, LDS film number 0106416.
QUAYLE, William 1817 Bal E 2 0106419
QUAYLE, William 1822 Bal A 41 0106243
QUAYLE, William 1830 Bal E 1 0106430
[from Brian Lawson's index].

There is a decree for Margaret Quayle als Cowley of Ballaugh in 1783 which should name all the children, so would show whether Philip b. Ballaugh was alive at that date, but is too early to show whether he was the one who went to Maughold. As previously mentioned, someone has put a death in 1773 on the IGI for this Philip, so her decree (and the parish register) needs checking.
It would be well worth ordering this decree anyway, for further information about the family which could well be yours.

All five films could be ordered at the same time.

I would also order the parish register for Ballaugh on LDS film, and go through this carefully looking at bapts marriages and burials for the family. LDS film no.0106707.
Brian's burial index and FamilySearch IGI bapts and marriages would help locate these, but I'd look through the whole film for ones which might have been missed or misspelt.

Although these parents look very likely you can't be 100% certain unless you find supporting information.

Sue