Perhaps there is more than one Henry Brougham.
Found no birth records for any Henry Brougham's but since the first Brougham record of birth was not till 1846 then that is one explanation. The source I use covers most counties in Ireland but not all.
There is a Thomas Henry born in 1873 Waterford but possibly the son of the 1881/1894 Rev. Henry Brougham?
The only ones I could find were years away from 1831 and perhaps following a family tradition?
1894 Very Rev. H. Brougham D.D. Church of Ireland, Diocese of Lismore
1881 Rev. Henry Brougham, sub-dean and pastor
1837 Lewis Topographical Dictionery gives a good description of Lismore and the church (cathedral)
Tallow has its own website and information through the
www.waterfordcountymuseum.orgWhich mentions Rev. H.Brougham who died in 1832 St. Catherine's Church of Ireland which was closed in the 1960's. There is a nice picture of the church.
No further mention of Henry.
Perhaps the Library or a letter to the museum might get you more information.
You can find the library of Waterford in a link from
www.censusfinder.com United Kingdom+Ireland+Waterford
you might find some other information on:
www.igp-web.com + Waterford
www.ireland.anglican.org The Representative Library of the Church of Ireland. They may well know where records concerning their clergy are stored, I would say likely there but not sure, I have been there to look at Parish records but for Wicklow.
See if a local History Society has recorded any Waterford
memorial inscriptions as often they print journals with these.
Annette Code