You should determine their religious denomination, if any. That may narrow the search.
Look for where other family members are buried. You may be able to use Findagrave, or Billiongraves websites to help with that. Or look for family funeral notices in Evening Times, Citizen or Herald.
Sighthill or Lambhill Cemeteries are closest to that Hospital, but that may be no indication of burial location.
Of course, it may have been a cremation...