are you saying there are only 5 wires at the back of your 6 pin plug? the 12v may be another color.

if a 12v wire is not avaliable at the harness on the tahoe, youll need to run a wire from the battery to the plug.  10 gauge wire with a 30 amp breaker would be appropriate, zip ties to hold it and wire loom to protect it, along the frame on its way back to the plug.  nothing to it.

who put the 6 pin on the tahoe?  id be a little hacked if someone did half a job.

well this is sort of difficult not being there and all, but white is generally a ground, and post 1 on my 7 way rv plug chart is also a ground. do you have a red wire on the back of the plug?

also you stated there is no wire on the center pin, if im not mistaken that is for the "backup lights", strange but probably not relavant to this situation.

now im going to take a shot in the dark (pun intended) here....  on my 2002 chevy trailblazer the 12v hot wire was not connected to the fuse block under the hood, as it came from the factory. as i came to understand it, after hours of cussing, tracing wires, checking fuses and haynes manuals, etc this was to keep newbie trailer pullers from discharging the trucks battery by leaving something on in the trailer. 

i would suggest checking the owners manual for the location of the trailer power fuse, on mine it was marked only "trailer fuse" and is a 30 amp.  if its under the hood, check if there is a stud next to the fuse, and possibly a ring terminal on a red wire in the general area.  now im not telling you to start touching wires to the battery, im only sharing my experiance.

I don't know if you still checking this but chevy usually leaves out the fuse that powers the internal lights on your trailer. I'm not sure if thats the case with your rig but it's worth checking. I bet it's not there. If you swing by your local dealer they should throw one in for free.

Good Luck,

cs