Trailblazer aux power outlet

wrong fuse , the service manual covers all that.
aux = old cig cigar jack in cab ? <<<< names change in time
but is the same CIG port, for sure.
the manual calls it

Horn/Cigar Lighter/Power Outlet oh, so horn is dead too,, sure.
fuse 15 is front CIG
read outlet (omg 2) is fuse 6 , 50amps that feeds FUSE B
fuse B is 20 amps and feds aux rear center pin power.out.

fuse B box name is RELAY and fUSE BOX RFB.

Some of the outlets are on the aux fuse in the passenger compartment, and the others are on the AUX PWR fuse in the fuse box near the battery.
Your owners manual should list the fuse locations.

The fuses for the auxilliary power outlets are located in the rear fuse panel located under the left second row seat.

The fuse for the console and two front outlets is fuse #46 (20 Amp) and is marked "AUX PWR 1"
The fuse for the rear power outlet is fuse #15 (20 Amp) and is marked "AUX PWR 2"

# 6 under hood, if this does not work, then under dash fuse # 30

a defective outlet

Have you checked the fuse box under the rear LH side chair?? This is where the fuses for the outlets are. Hopefully this helps

CIG LTR Fuse 15 amp located in the under hood fuse box. Plus AUX PWR 1 fuse 20amp also located in the underhood fuse box.

the problem is always the lighter or lighter receptacle

Replace the Aux Pwr fuse. On the 2008 Equinox, this fuse is in the fuse block under the hood. It is fuse number 3, 20A (yellow), located on the left side as you're looking it, in the slot immediately forward of the fuse puller tool. Way too late for Kevin256, but I just did this on my daughter's '08 Equinox and it fixed the problem.