Hi Sunnydaze,
You have a time and (probably) money consuming task to try and resolve. Assuming the boys were both born after the marriage of their parents, then to find by male of surname Clark, probably born in Fife or Dundee area would mean looking at many birth certificates, probably from 1916 to 1919. To do that online would bankrupt you very quickly. It can only be done economically by going to the ScotlandsPeople Centre in Edinburgh, or one of its outposts around Scotland. Unfortunately there is no such facility outside of Scotland.
If you are within travelling distance of one of the SP Centres, then fine. Otherwise, you will need to seek someone's help to go to one of the SP Centres on your behalf. In the SP Centre, you pay an entrance fee for a day's search time. You can look at as many certificates as you can fit into the time during that day, for no extra fee (unless you print off the certificate - for births only allowed for certificates more than 100 years old). Printing incurs a cost; copying down the details by hand (writing or your own computer) is free of charge.
If I was doing this search, I would start with the first name of John Clark's father. If they used the traditional Scottish naming pattern (many did this), then the first son could well be named after his paternal grandfather. If they followed this tradition, the second son could be named after his maternal grandfather. However, be prepared for them not to have followed the traditional naming pattern, and their names could be anything.
The other option is to wait 4 years. In 2021, the 100 year closure of the 1921 census will expire. All going well, that will show the parents and surviving children; and a count of children born to the couple (hence you also have a count of children who died prior to the census).
All the best,
AndrewP