This evening, I've tried the following searches for Alex Davidson son of John Davidson and Margaret Wilkie, and none returned any possible match:
Any male birth, with surname DAVID*, born in Cruden or Peterhead, 01/01/1837 to 31/12/1842
- no Alexander born to a John
- no Wilkie
Anyone, with surname DAVID*, born anywhere to a WILKIE, 01/01/1538 to 31/12/1854
- only one Alexander, but father's name is George Davidson, mother's name is Janet Wilkie, and born 1835 in Angus.
- no fathers named John
Any female death, forename MA*, surname WIL*, other surname DAVIDS*, between 01/01/1538 to 31/12/1854 (I know from Alex's marriage certificate that his mother had died by 23/02/1869)
Any female death, forename MARG*, surname WILKIE, other surname DAVID*, between 1855 to 2009.
- this search returns the closest possibility, but not close enough. Margaret Wilkie (married name), father's name Alexander Davidson, married to a William Wilkie (seaman), died 1861 at 83 years old in Banff. Age 61 at time of Alex's birth. Just coincidences.
- Remaining three all died 1913 or later.
Any death, forename MARG*, surname WILKIE, (no other surname), between 1855 to 1869.
- one Margaret Wilkie died at age 93 in 1864, in Aberdeen City. Would have been aged 68 at time of Alex's birth.
- No others.
Anyone, with forename ALEX*, born anywhere to a WILKIE, 01/01/1837 to 31/12/1842
- only one to a Margaret Wilkie, father's name Alexander Bennet
- no Johns
Anyone, with forename ALEX* and surname DAVID*, born anywhere to a JOHN, 01/01/1837 to 31/12/1842
- no Margarets
- no Wilkies
- no unrecorded mothers
I also discovered today that my great-uncle had told my mother that Alex Davidson went to Monikie from Arbroath at the age of 15. My mother thought Arbroath is in Aberdeenshire, and consequently told me that Alex came down from Aberdeenshire to Monikie (no mention of Arbroath). However, the censuses I do have for Alex do indicate that he was born in Cruden or Peterhead.
I'm completely lost now, there seems to be no record of his mother's existence, or of anything that could be his birth. Is it possible that he didn't know one or both of his parents' forename/surname? Or that he didn't know where he was born? Or could there be a more complicated reason? Or am I missing something obvious? Or is this just a dead-end, with no way forward?