This happens in the bright and dim modes? If so, it may be a high resistance in the ground of the left head light. The ground is beside the battery on the left fender. I would clean that ground and make sure it is clean and tight.
As crazy as it sounds, the only thing I can figure, is that maybe the left headlight circuit has a higer than normal resistance. When the altenator power is not under a heavy load, the light can pull enough current to work ok. But under a load, the higher resistance wins out and causes the light to dim.
I am just guessing here, but try and make sure the light has a good ground, and then maybe have the altenator checked to see if it isworking properly.