Wire size? Pretty light (maybe 14g). Seems super light in retrospect but that was the same gauge as the make-a-tap fuse connector thingy.
Tow vehicle had a 4-pin so I had to wire in 7-pin for the trailer brake controller and to get power back there. Looking at a 7-pin diagram again you're right those lights come through what were those original four pins.
It's the amp drop thing that gets me and I can't be back there to see it. I just presumed watching at startup it's at 2000 RPM I get the alternator spinning and at idle I get back down to the minimal feed. Still means I'd be great running in 4th gear all day. Maybe I get the bluetooth dongle for the BVM so I can see it on the road.