MorningStar inverters are top-quality units! Excellent choice!
Just to reinforce what you have heard so far;
The 3-light circuit tester is simply indicating that the receptacle's neutral pin is not bonded to ground. This does NOT mean that there is a problem with the connection between the ground pin and your chassis ground of your TT (although it doesn't mean that it's intact either). If you are concerned you can simply check for continuity (ground pin to chassis) with a VOM, with the inverter OFF.
The National Electrical Code requires that the neutral and ground be bonded at only one location. This is to prevent "objectionable current" from flowing on the ground conductor. If you are plugged-in to shore power then the ground at the shore power outlet should be bonded to ground (only) at the main service panel... and the two yellow lamps on your tester would be illuminated when you plug it into an outlet inside your TT.
IF you were connected to a true Earth ground (e.g. copper stake), and NOT connected to shore power, you could safely bond the ground and neutral pins inside your "30 amp RV style female receptacle" (such that the neutral-ground connection was broken when the adaptor was removed) at this one location and the tester would show 2 orange lamps.
Note that OSHA specifically permits vehicle mounted "generators" (ie. your inverter) to use the chassis as a "ground" instead of Earth IF the loads you are operating are plug-and-cord connected to your generator and the generator housing is bonded to the chassis.
My ProSine "not junk" inverter is configured to have ground and neutral UN-bonded in all modes of operation and my Honda EU2000i does not bond ground to neutral either.
Hope this helps.
Cheers
-Mark
