I'm still reeling at the co-incidence of the 1854 County Mayo marriage, given the groom's name, the bride's surname, their occupations and fathers' names and occupations, but co-incidence it remains at this point, for I can see nothing more than that.
If the only source for Henry's father being called William is what an informant provided at the time of his death, then I would be open minded about that, for such information can be notoriously inaccurate and besides that, there is always the possibility the father was William John or John William.
The surname Giltrap isn't common in the all Ireland context but the small numbers overall are not widely dispersed, when you look at Griffiths Valuation and the 1901 and 1911 census returns, besides odds and sods the majority are clustered in counties Carlow, Wicklow and Kildare, with some spread into Wexford and Dublin, the latter probably for economic / work reasons.
Very slim pickings from me, but just to note a couple of marriages where the father of the bride or groom was recorded as John Giltrap, a teacher (can't see any for a teacher father called William Giltrap). As it happens, they occurred in County Wicklow.
Firstly, Thomas Giltrap, a teacher (son of John Giltrap, a teacher), married Mary A. Giltrap in the Church of Ireland on 30 November 1863, both were from Mullica / Mullycagh, a townland in the civil parish of Hollywood (Lower or Upper I don't know - some of the previous posters on this thread mentioned this townland). Given the recorded age at the time of marriage, Thomas would have been born in 1839. This looks like a possibility for them in 1901 and 1911:
http://www.census.nationalarchives.ie/pages/1901/Wicklow/Dunlavin/Toberbeg/1808671/http://www.census.nationalarchives.ie/pages/1911/Wicklow/Dunlavin/Toberbeg/889161/Secondly, Jane Giltrap, a teacher (daughter of John Giltrap, a teacher) married Robert Giltrap in the Church of Ireland on 5 May 1870 (Hollywood parish), again both were from Mullica / Mullycagh. A Thomas Giltrap witnessed. As I said, not much to offer, but at least you know there was a teacher called John Giltrap, very possibly from the Mullica / Mullycagh area, in the first half of the 19th C. Given that the name Giltrap isn't common and that the teacher occupation should reduce the field, here's hoping you get more replies...