Margaret (Johnston) Falconer was my 3rd great-grandmother, and she's become a brickwall:
Her marriage on 12 October 1858 lists her husband's parents, but not hers, just says that they were both of the same parish (Newcastle).
In the 1861 Canada Census, Margaret and William and children are residing in Newcastle: https://www.bac-lac.gc.ca/eng/census/1861/Pages/item.aspx?itemid=2082235 and the same in 1871 (albeit with the surname spelled incorrectly): https://central.bac-lac.gc.ca/.item/?app=Census1871&op=img&id=4396660_00599
Margaret and William both died in the spring of 1879, approximately three weeks apart: https://www.findagrave.com/memorial/133881593/margaret-falconer.
I have no idea who her parents were, or how to find them, I haven't yet turned up a baptism or a birth record for her.
Hi Stu! Based on the headstone and this, transcribed from a New Brunswick paper: https://archives.gnb.ca/Search/NewspaperVitalStats/Details.aspx?culture=en-CA&guid=d80ba2ec-493d-4f4f-9845-06d15bf28f5c.
1879 - 45 = 1834 (or 1833, depending on when her birthday actually was).
I'm somewhat confident of her birth year, +/- a year or two.
My 4th great grandmother is Charity (Falconar) Barnes. I just ordered the Falconer of Halkerton book from Amazon and it covers all the male lines beginning with Alexander Falconer of Halkerton, who died about 1499. It goes into the branches from Scotland, to England, the United States and Jamaica. When it arrives, I will check to see if your Falconer line is included. The book is due to arrive November 24th-December 20th.
I know my Falconer line (see: Falconer-1627) came from Kincardineshire before they settled in Canada and they really liked the name 'William', I'm not sure how/if they connect to the Halkerton line. Let me know though, please!