I never would have thought of the Inverter, especially since it is off where we are now camped. It's very quiet here, so the fan is more noticeable.
My 2010 2551 has the newer Xantrex inverter like yours, below is an old post of mine that addressed the same issue of the inverter fan running when not in use. Hope this helps.
Yes Billy, I turn off the inverter at night by turning off the breaker that supplies 110vac to the inverter. I too was bothered by the inverter cooling fan cycling during the night. I did some investigation because it seemed strange that the cooling fan would run when the inverter was not being used at night.
On the 2551, the inverter is located under the passenger side bed and is mounted forward of the converter/breaker panel on the same wood panel. First I had to determine if I was hearing the converter fan or the inverter fan. The converter fan will run if you are plugged into shore power and are using a lot of 12vdc or are charging the batteries at a high rate. You can feel the air flow in the grill on the converter/breaker panel when that fan runs which it turns out is not that often, and I have never heard it at night. If you hear a fan noise from under the bed and you don't feel or hear the converter fan running, then it is the inverter fan.
The inverter cooling fan should run when it gets warm from working to create 110vac from the 12vdc batteries, although I don't hear it often when running it to watch TV since the current draw is low. But I was hearing the inverter fan run when it was not in use. I replaced the inverter (thanks Kermit) and the new one behaved the same. So I contacted Xantrex a few times and finally found someone who explained that the inverter cooling fan is designed to come on periodically even when not in use to cool the internal switching relay that automatically switches from shore power to inverter power. I guess the relay is "on" and passing the ac supply through the inverter when the inverter is off.
So, at night, if you switch off the breaker that supplies the 110vac to the inverter (not the breaker that comes from the inverter), the fan will not run. You also have to turn the inverter control panel off or the inverter will now use the batteries to keep the TV and DVD player on standby.
Since I love a challenge, I decided to rewire the ac side of the inverter and installed a switch so that I manually put the inverter on line when needed. So now if I want to use the inverter, I have to press a switch that I installed on the wood panel under the bed in addition to the inverter wall control panel.