Location of a +12V wire at rear seats/trunk for inverter?

[ThinkPad]

I have a 12V > 230V inverter that i would like to use during holidays and such. Unfortunately my 2006 Yaris only has a cigarette lighter outlet underneath the cooling/heating knobs.
Would have been nice if it had a secondary outlet available at the rear seats or in the trunk, but it's not there.

My Yaris has a towhook and electrical outlet for the lights of a trailer (7pins EU system) but i'm not sure if it carries a +12V. Some diagrams say that it has a constant voltage pin (for running a refrigerator in your caravan while driving for example), but later on it was changed to drive the foglight of a trailer.
I will get my multimeter and see what it carries and if it is a constant voltage, see if i can tap into it underneath the carpet of the trunk.

But should it not be available, is there maybe a different wire running to the back, to tap into that can handle about ~10A max. ? I prefer a wire that is turned on/off with the ignition.
I searched for a wire schema of a 2006 Yaris, but couldn't find it.

I also thought about soldering a wire to the cigarette lighter outlet and running it to the trunk, but that involves quite some work by lifting carpets and such.