The converter should keep the voltage constant given your present situation
Additional load more lights, water pump, heater blower, the lights should not flicker, maybe dim just a tad for a tiny moment but not enough to notice undress you are looking at the light when it happens,
You have one or both problems, battery or converter
Turning" on a high amp 120v load will only reduce the input voltage to the converter, and should not flicker the lights except when the batteries are shot and the the DC power is really coming from the converter and the batteries can not supplement when the 120v load changes (bad battery-batteries) or the 12v load changes
Doug how often does the No Frost heater strips in the fridge doors cycle, I don't think it's a heavy load, trying to eliminate suspect loads via timing occurrence, how often would the ice maker cycle
Anything that can be turned off for testing may help solve the issue, by process of elimination
