The birth states "Isabella Haig Stevenson is Wesley Cottage, Parish of Gamrie and that John Duncan was Parish of Banff"
From that, I don't think he was born Gamrie.
That's a reasonable set of parameters, but in practice I don't think you can deduce anything with certainty.
When John Duncan signed the birth certificate he would have been asked where he was currently residing, so he could have been born in Timbuctoo or (worse) England or USA, and residing at Backhill in the parish of Banff.
All you have to go on with certainty is that his name was John Duncan, that he was a farm servant, that he was old enough to father an illegitimate child in 1938, and that at the time of the child's birth he was residing at Backhill in the parish of Banff. You can deduce that he was a decent sort of man because he owned up to fathering the child, even if he never actually married the mother.
There were 1,399 John Duncans in the 1911 census in Scotland. Even if you eliminate the ones who were too old and the ones who would have been old enough but died, you still have to add on any born between 1911 and say 1920-ish.
It is likely that John Duncan was born in Banffshire or Aberdeenshire, but that on its own is not enough to pinpoint him. The words haystack and needle, not in that order, spring to mind.
Does the handwriting of his signature match the handwriting of the rest of the certificate you have? If it does not, then you are lucky, because the registrar sent the original register to Edinburgh and retained his duplicate register (into which he copied the signature), and what you see is John Duncan's own handwriting.
You could then look at marriages of John Duncans from 1938 onwards, and see if you can find one with a matching signature. I cannot think of any other reliable way of pinning him down with 100% certainty unless you can find a descendant who has some more definite information about him.
