Excessive electrical draw?

My 2020 Mallard M301 when the gas heater blower starts half the interior led lights inside go very very dim. Once the heater blower stops, the LED lights return to normal brightness. The furnace seems to work fine with warm air coming out of the heat vents. The lights that dim are the ones over the kitchen counter, over the couch and recliner chairs as well as the ones over the headboard. All the ceiling lights, dining table light, bath lights and bedroom ceiling light and the outside door light work fine. I suspect that either the blower motor is drawing too much power OR the control board is going bad. Anyone have any suggestions on how to diagnose the problem and replace the bad component? Thanks.

Is this a new symptom, or the furnace motor has never caused these symptoms before? How is the health of your batteries and have you measured the voltage during the brown out?

Brand new problem. The battery is less than a year old with only two camping trips on it, both trips with shore power.. Due to very inclement weather I have not tested the battery other than to check and make sure all the cells had water (they did). All my other electrical appliances like the refrigerator and the overhead lights work perfectly with no apparent issues even when the furnace blower starts. The furnace seems to be running fine with no electrical burning smell and is keeping us toasty warm during this very cold weather spell. I should also mention that I am hooked to shore power with a voltage regulator/surge protector on the line.

Even though the battery is relatively new the first thing I would do is to have it tested to be sure.

Next I make sure your converter is working by testing the voltage across the battery while on shore power. Should be around 13 volts.

If that all checks out I would check all the ground wires (including wire nut connections) to ensure clean tight connections. Also check the frame ground.

As Bogie said above check those grounds