Thanks for the compliment, but I think it's just that I've been doing this too long. The electrical socket is going to be more limited by the fuse, then the socket itself. I think it's like a 10amp fuse on there. Cell phone, GPS chargers, radar dedectors, etc use almost nothing, so it's not an issue. The power inverter might suck over 10amps though. Those things can use quite a bit of power. How big is your power inverter?
The autoparts store cigarette lighter will not hook up to your standard plug. I solder everything, but I'm not sure if you are set up to do that. It's a good idea to put a new disconnect plug in there, so that if you have to take out the shifter bezel, you don't have to cut those wires and reconnect them afterwards. You are going to want to find a generic cigarette lighter with 2 wires coming off of it. There is a little electrical plug in the towing section with either a red and black wire, or a red and white wire. It's usually $2 or $3. You can solder that inline with the factory wires to replace the factory plug. The cigarette lighter has a bezel on it to keep it from pushing through the plastic. If it doesn't have suitable clips on the back of it to keep it from pulling out, you can hold it in there by putting a hose clamp around it.
Kurt