Hi,
Thank you all for your prompt responses.  My last attempt to trace this Robert Gray was three or four years ago.  I am planning a trip to Shetland, then Edinburgh and thought I would try again.
1.  I have been in correspondence with Glasgow University, also spoken to a librarian at the Mitchell Library.  However this Robertus Gray throws up another possible spelling that I haven't come across.  I was led to believe that he didn't graduate.
2.  During that time I read his entry in the Fasti, corresponded by email to Presbytery of Hamilton, the Church of Scotland and eventually the National Archives - all without success.
3.  I understand that the National Archives have digitised the Presbytery Records and these are available to view in certain libraries throughout Scotland.  I  have located the reference number for the Presbytery of Hamilton which is CH2/393.  Problem is that I live on the South Coast.
4.  I have sent a request to the Shetland Archives since they are one of the Archives that have such access.  I will post details of anything I receive.
A question - what would I expect to find in Presbytery records for that period?  I am hoping that it might give the names of his parents.  He is a 6th great grandfather on the paternal side of my maternal tree and a brick wall for many descendants.
Thank you once again.
Kind regards,
John Robertson
www.shetlandroots.org