Doug,
Griffiths Valuation for 1860 lists William Gilmore in Drumardnagross. He had plot 7 which was an 13 acre farm. Today that property is down a minor lane off the Mullagh Rd, a mile or two north of Trillick.
http://www.askaboutireland.ie/griffith-valuation/index.xml?action=nameSearch
The Valuation Revision records show that he later acquired plot 8 making the farm about 26 acres. William is replaced in 1882 by Robert Nealands. There are further changes before James Gilmore appears as tenant in 1911. He is replaced in 1914 by Hugh Thompson.
William Gilmore died on 26.7.1880, aged 85. He was a widower.
https://civilrecords.irishgenealogy.ie/churchrecords/images/deaths_returns/deaths_1880/06467/4859979.pdf
https://www.nidirect.gov.uk/services/searching-valuation-revision-books
There was a Joseph Gilmore working as a farm labourer in 1911. Not sure if he is connected to the family. Possibly not.
http://www.census.nationalarchives.ie/pages/1911/Tyrone/Trillick/Drumardnagross/869924/
Robert Gilmore married Ellen Gilmore on 22nd Feb 1855 at Dromore Presbyterian church.
Matilda Gilmour married Robert Patterson on 16th July 1856 in Dromore Presbyterian church.
https://churchrecords.irishgenealogy.ie/churchrecords/
Tradition was to marry in the bride’s church, so that suggests the Gilmore family church may be Dromore Presbyterian. That church’s baptism and marriage records start in 1835. There’s a copy in PRONI in Belfast.
Sarah Jane Gilmour married Gerrard Todd of Esker on 9th Mar 1859 again at Dromore Presbyterian. Robert Gilmour was a witness.
The Gilmore/Gilmour family being Presbyterian would fit with their ancestors having come from Scotland. Huge numbers of Scots settled in Tyrone in the 1600s, so that’s not uncommon. Presbyterianism was established in Scotland in the 1500s and brought to Ireland by Scots settlers.