You definitely need to start on Scotlands People with purchasing the birth certificate of your grandfather John Davren b.1936 Camlachie to definitely determine the names of his parents.
If, for instance, it was as you suggest and that his parents were a John and Sarah there is only one marriage between a John Davren (indexed on SP as Davrin although quite clearly Davren on marriage certificate (had a few credits left) - however, this John wasn't the son of a John!
John Davren, Motor Lorry Driver, 23, son of Arthur Davren and Helen Hosie and Sarah Cunningham Winning, 20, dau. of George Winning and Annie Cunningham, married 12/6/1931 Calton, Glasgow.
So, this dispels the belief that you come from a long line of John's and also that your grandfather was the youngest of 6 since he was born 1936 and John and Sarah had only been married 5 years at this point.
However, the most important thing is to make sure you set off on the right foot and that is by purchasing a copy of your grandfather's 1936 birth certificate to definitely determine who his parents were. (It may indeed have been John and Sarah - who can say at this point - but family beliefs can get confused over the years . There are, for instance, 3 birth entries for a Helen Hosie Davren - one in 1921 Bridgeton (dau. of Arthur and Helen?), one in 1936 Provan (same year your grandfather born but different place) and the third in 1940 Bridgeton.
Annette