Now, regarding your power issue, first I suggest you don't use the 110 inverter for several reasons:
- I doubt there's enough wattage in the factory inverter in the right rear to power your fridge.
- With vehicle accessories that either a 12 VDC or 110 VAC, it is always better to avoid the inverter if one is able to use the 12 VDC cigarette lighter socket. I puts less strain on the electrical system, especially if one want's to keep it accessory running with with engine off.
If you go to my build:
Builds - R2M 2013 GX 460 Expo
It will show how I added a 3,000 watt inverter and a panel that has one 12 VDC cigarette lighter socket, two high speed USB ports and a voltage meter.
Note: First off, I have dual batteries. I used 1 AWG gauge wire that ran along, tucked up behind my rock sliders and connected to my second (house) battery. I added the panel with the 12 VDC accessory ports to the pop out access panel for the bottle jack and tapped into the 1 AWG wires that went into my inverter.
Now if you don't want to do the dual battery thing nor add a big 'ol womp'n inverter, then you can still use a much lighter gauge wire and run it straight to your battery.
This is what I purchased from Amazon:
Amazon product ASIN B078K9NW7XIt nice because this panel also has a power switch so I can turn it off when not needing to use the power when I'm away from the vehicle or over night. I'm also absolutely sure I'm not getting any battery drain of any kind. Using the access panel makes installation super simple since you don't have to pull and pry any interior panel to install!