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This is what the indexes to the original records show.

John Baird and Helen Watson were married in Glasgow in 1817. Their family were
Archibald, baptised 1818 in Mauchline
Jean, baptised 1820 in Leith
John, baptised 1822 in Leith
William, baptised 1824 in Greenock

In 1841 the family, minus Archibald, were living in Meadowbank, Edinburgh.

Have you viewed all the baptism records? Are the witnesses' names recorded, and if so do they provide any clues?

Archibald Baird and Agnes Bell had eleven of a family, five baptised in New Cumnock then six baptised in Mauchline. If I were you, I would be looking at some of those baptisms to see if they resided in the same place where John B and Helen Watson were when their Archibald was baptised.

If Findlater is a rare name in both Ireland and Scotland as suggested there should be a common connection to form the relationship somewhere.  Maybe the whole family didn't move to Scotland during the early 1830's.

I'd say it was uncommon but not rare. Scotland's People has 12,512 references to Fin*l*t*r.

The name originates in Banffshire, where there is a ruined Findlater Castle - see https://www.geograph.org.uk/search.php?i=211308948. It was a seat of the Ogilvies until they built the more commodious Cullen House in 1600.

For those who don't know "Jack" is the pet name for "John" and the English equivalent of the French/Norman given name of "Jacques".

Actually Jacques is the equivalent of James, originally Jacob, becoming Latin Jacobus, which mutated to Jacomus and became Giacomo in Italian and James in English.

John is the equivalent of French Jean, and Jack was almost always a pet name for John, via Jan, then Jankin, though it's now used as a separate name.

Burial records are normally held by the relevant local authority. I believe that Eastwood comes under East Renfrewshire Council https://www.eastrenfrewshire.gov.uk/ so that is where to start.

I came across a Joseph Burgess or Fell, illegitimate son of Jean Burgess, father's given name unknown, baptised 29 June 1789 in Middlebie, Dumfries-shire. He obviously doesn't fit any of the ones in this thread, but Joseph isn't all that common a name so it's not impossible that there might be a connection.