Had the same problem. Lights would slowly dim intermittently and stay low 10 to 30 seconds, then slowly come back up. The transition high to low and low to high would take as much as 20 seconds. Didn't seem to be related to temperature, load or vibration. Sometimes it would go 10 minutes between "dips", sometimes it would dip again immediately. I was suspecting both the battery and the converter, and trying to determine which it was, when I caught the voltage going low with the battery disconnected. Replaced the converter - all is well.
An intermittent heavy load causing the voltage to go low (or an auto-reset breaker tripping in and out) would likely show up as an instantaneous change, not a slow transition.
So, if your transitions are slow, I would put my money on the converter.