Hi Red32,
'Finkilragh' is actually 'Finkiltagh' (the National Archives have mistranscribed the 1901 census).
Adam Thompson of Finkiltagh has a headstone in Portglenone CoI Graveyard:
'Erected By Adam Thompson Finkiltagh In memory of His daughter Isabella who died 20th March 1881 aged 6 years Also his son Samuel who died 28th November 1896 aged 58 years [this is almost without any doubt a mistranscription: I suspect Samuel was '28' when he died] Also the above named Adam Thompson who died 6th October 1902 aged 72 years And his son James who died 30th May 1908 aged 50 years'
Based on the names of his children (from the above headstone and from the 1901 census) it looks pretty certain that Adam's wife had been Jane Mill(e/a)r. Adam Thompson married 'Jenny Miller' at Buckna Presbyterian in 1858: his father was Henry Thompson and her father was James Miller. I believe Adam and Jane/Jenny were from the Buckna/Racavan area originally but later settled in Portglenone. Adam's father Henry Thompson died aged 93 in 1881 in Ballyligpatrick and left a detailed will (which you can see online for free on the PRONI site) which mentions Adam and a number of other siblings.
Amazingly, at some point in the early 1900s the census records for 1841 and 1851 were trawled through by someone interested in the Thompson and Thomson families of mid-Antrim and the extracts have all survived and are held at PRONI: the 1841 census of Ballyligpatrick found Henry Thompson, aged 48, a carpenter; and his wife Nancy Graham, 44; and their children: Nancy (20), Henry (15), Sarah (13), Adam (11), Robert (9), Jane (7) and William John (1). Robert Thompson (aged 9) in 1841 later emigrated to America by the time his father died in 1881. All of the children mentioned in the 1841 census seem to have still been alive by the time of their father's death except for Sarah (she was the only one not mentioned in Henry's will).
Hope this helps!
Best wishes
