That converter may not be the best, but I agree with the conclusion by others that it is acting like the Microwave and the A/C that you cited. In other words, I, too, think the 12VDC lighting is misbehaving because the 120VAC that the 4KY supplies to the Converter is misbehaving. If Converter IS MagneTek, all it has is a switch powered by 120VAC to take over the 12VDC load from the Battery. If the 120VAC is fluttering, and makes that switch flutter, then your lights will be flopping back and forth from Battery Power to/from Converter Power.
I still suspect a problem with the 4KY. Had it been running well? Recently?