Not sure to understand what you mean about the 110v inverter, but I have the factory 110v inverter in mine and the inverter is also a SWITCHED device!
I do not experience myself on installing a remote start or alarm, but on every specific installation guide for Compass/Patriot I found, they all stated you must ran a wire directly to the battery for the un-switched 12V power... I also check on the famous "Bulldog Security" website and they also say you need to ran a wire to the battery or use the TIPM module but it's useless...
I'm gonna install my remote start in a few weeks before the winter so I'm gonna be able to confirm this information, but honestly I think it's true.
In fact there's no dedicated switched power source neither in the fuse box, but when I replace my factory radio for an aftermarket, I just hook it up to the cigarette lighter and voila! The 60-80$ radio interface is a scam, i just provide the missing switched circuit when the cigarette lighter switched circuit is just 2 inch below the radio! The cigarette lighter circuit is also R.A.P. enabled, so my aftermarket radio work as the factory radio without any lost of feature!
In my Chevy Cobalt there's no switched source for the radio neither and the cigarette lighter is un-switched as I said, so I hook my radio switched wire onto the windshield wiper circuit (switched and also R.A.P. enabled) and voila! I also save on the 60-80$ radio interface and I even have the RAP feature.
