I never found a birth record for John. He may have been christened under his father's name.
The only way I can suggest to find this, is to run down the mothers' names on Brian Lawson's birth index, looking for Sarah Taggart,
I suspect that in the 1891 census, he is the nephew at Athol Cottages in Douglas RG12/4687.
Ann Qualtrough head single 47 charwoman b. Arbory
Thomas Gale 9 nephew scholar b. Arbory
John Taggart 6 nephew scholar b. Douglas.

In the 1871 census Sarah Taggart is in Colby Village Arbory RG10/5778
Jane Qualtrough head Widow 69, Ag. Lab b. Patrick
Ann Qualtrough Unmarried daughter 28 b. Arbory
Sarah Taggart granddaughter 4 b. Malew
Elizabeth A Spense 7 granddaughter b. Patrick.

I did not find a suitable Sarah Taggart in the IGI but there is a christening record in Arbory for a Sarah Qualtrough, daughter of Ann Qualtrough (no father's name) on April 19 1867.