Their eyes usually run because the tooth roots are pressing on the tear duct. Trimming his teeth regularly won't help with this although it is extremely important you still do this, it will just keep him feeling 'comfortable' in his mouth. My bridge bun Sox suffered with runny eyes alot because of this , he had to have the tear ducts flushed a couple of times to help aliviate it along with having regular dentals because his teeth were awful. Has your bun had a head x-ray?