I start repeating information hoping the extra probe finds something not known to you
Robert and Ellen marriage by license in the parish church of Rathmullana church Wed 26th Feb 1862 Robert in his marriage signed with his mark. Ellens address was Killough village itself and her father Joseph the two witnesses were Benjamin Robinson and William murphy.
The day before 25th Feb 1862 Arthur and Catherine married at the Registrars office in Downpatrick both signed using their mark and witnesses james feagan and Ellen Smyth dau of john smith
from
http://www.rosdavies.com/SURNAMES/D/Davidson.htm for Bright Davidson
DAVIDSON family Bright living in Carman's Row, Killough c. 1900 KCL p 25
Mr. DAVIDSON Bright a farmer;living in Castle St, Killough c. 1900 KCL p 24
Arthur DAVI(D)SON. Down & Bright son of Arthur Davidson ; married Catherine Smith/ Smyth 25 Feb 1862 in Downpatrick; father of Catherine b. 18 Jun 1865 & Ellen Jane b. 8 May 1868 & Arthur b. 1 May 1873 (regd. Killough) note WHY HAS THIS ENTRY STARTED WITH DOWN ?
because he married in Downpatrick presumably because Catherine his spouse lived there or for other reasons. you could go down all the Davidson Down entries if wondering any other reason eg a mixed Christian marriage etcMrs Ellen DAVIDSON. Bright of Killough; a grocer in 1910 POD
Miss Hazel DAVIDSON. Bright danced at a concert in Killough 11 Dec 1926 DR*
Mrs Jane DAVIDSON Bright of Killough in 1910 POD
Miss Mary Jane DAVIDSON. Bright married William Pollock 1873; sister of Ellen; mother of Arthur LR 2007 p33,34
Mr Ralph DAVIDSON . Bright of Ballycam; won 2nd prize at Ardglass motor treasure hunt 12 Nov 1937 DR
Robert DAVIDSON DAVISON Rathmullan & Bright son of Arthur Davidson; married Ellen McCullough 26 Feb 1862 in Rathmullan ; father of Robert b. 19 Sep 1864 & Margaret b. 22 Apr 1869 & Joseph b. 29 Jun 1871 & William b. 16 Feb 1874 (regd.Killough) CR; Trudy Davison
there is an entry just one for Davidson in Rathmullan parish
Robert DAVIDSON DAVISON . Rathmullan & Bright son of Arthur Davidson; married Ellen McCullough 26 Feb 1862 in Rathmullan ; father of Robert b. 19 Sep 1864 & Margaret b. 22 Apr 1869 & Joseph b. 29 Jun 1871 & William b. 16 Feb 1874 (regd.Killough) CR; Txxxx Dxxxxxx
so we have Txxxx Dxxxxxx supplying information to Ros Davies, which suggests the spelling alternative entries Davison need to be investigated further than Txxxxs info eg
J.DAVISON .Bright a Protestant; father of Margaret (illegitimate) bpt. 8 Mar 1859 at the Catholic Church - mother was Mary Caulfield of Killough PR . Two Davison of Down listed in 1796 Flax growers etc . Txxxxx isnt listed under ros davies messages for contact details
TAB
http://www.irishgenealogyhub.com/down/tithe-applotment-books/bright-parish.phpDavidson no entries
McCullogh, James Townland: Kilbride Year: 1834
McCullogh, Jas. Townland: Kilbride Year: 1832
McCullogh, Joseph Townland: Ballycam Year: 1832
McCullogh, Joseph Townland: Ballycam Year: 1834
McCullogh, Ralph Townland: Kilbride Year: 1832
McCullogh, Ralph Townland: Kilbride Year: 1834
McCullogh, Robert Townland: Ballycam Year: 1832
McCullogh, Robert Townland: Ballycam Year: 1834
http://www.irishgenealogyhub.com/down/tithe-applotment-books/rathmullan-parish.phpDavidson no entries
McCullagh, Archy. Townland: St. Johns Point Year: 1833
McCullagh, Wm. Townland: St. Johns Point Year: 1833
McCullough, Archbd. Townland: St. Johns Point Year: 1833
McCullough, Wm. Townland: Killough Year: 1833
McCullough, Wm. Townland: St. Johns Point Year: 1833
http://www.irishgenealogyhub.com/down/tithe-applotment-books/down-parish.phpDavidson, Saml. Townland: Demesne of Down Year: 1833
Davidson, Widow Townland: Tullymurry Year: 1833
Davidson, Wm. Townland: Tullymurry Year: 1833
Davison, Joseph Townland: Demesne of Down Year: 1833
tried quickly
Genes Reunited,
a joseph mccullagh b 1861 co down tree holder peter
wikitree familysearch.org,nothing obvious
Church records
http://www.rosdavies.com/PHOTOSwords/BrightAll.htm#cathkill you have visited Rathmullan Church of Ireland in Rathmullan then Bright Parish south of Downpatrick , on Scollogs Road
however have you also visited or searched Bright Church of Ireland in Bright townland or other churches Have you discovered if familysearch.org microfilmed any records and are you aware of PRONI Belfast gave a downloadable guide to church records as does ros davies but they differ Ros adding in familysearch.org etc
have you seen the accompanying map for Arthur Sen and junior at St johns point rathmullan on griffiths valuation via askaboutireland ie
Arthur junior map ref 7 b in st johns point townland showing house valued at 10 shillingspa
Arthur senior map ref 7d in st johns point townland showing house valued at 15 shillingspa
where I also found Wm mcCullagh at map ref 2 with 6 acres land no house and Wm McCullagh junior 9 acres and house valued £1 five shillingspa the census 1901 shows mcullough 14 st johns point is C of I
hoping something useful for your quest
good luck onwards