Either you are doing something wrong here or I am misunderstanding what you are saying, get the voltmeter on a window line on the b plus side of the defogger glass, then get the gd side of the voltmenter on to the ground connector for the glass and see whats what. Make sure there are no breaks in lines also. If you have 12v at the glass lines and a good gd at the other end of the glass, then either the purple wire has high resistance somewhere so the amps don't reach the glass or your lines are bad in the glass. What is the connection with removing the relay and checking the glass ground?