Sounds like a voltage problem to me; higher the load, lower the voltage. Have you tried checking it when AC is off, low, medium and high? If the voltage does drop much, I'd look for a loose or corroded connector.
Another possibility is a bad switch.
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2012 Dodge C3500 DRW 4x4 Long Box, WeatherGuard 90 Gal transfer tank, B&W Companion Hitch
2012 Keystone Montana 3100RL, 520W Solar, 460AH batteries, Morningstar MPPT 45 CC, Bogart 2030RV monitor.
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