A problem with your idea is that the switch in question is an AC switch. That means that it carries 120V. This is good and bad. Good because it doesnt carry much current (4 to 5 amps or so) and therefore doesnt require wires with thick copper, but it carries a high voltage so you need thick insulation. You need to use wires and and switches designed for these voltages, and you need to ensure that nothing and no one will come into contact with bare wires of any sort.
What I recommend you do if you have the proper expertise is to use a 12 volt dc switch in your trunk to operate a relay that simulates your AC switch on your inverter.
Hope that helped.