I have run a charge wire from the front of my 1996 Suburban to the rear. The wire was already there from the factory, I just had to hook it up. And I have checked many times and it does recharge the batteries from 50% charge to full in the two hours it takes me to drive home from the desert.
Hopefully you have a multimeter and know how to check voltage with it. If not I would probably go to Harbor Freight or Walmart and buy a cheap meter. If you have a meter but don't know how to use it try to give us a name and model number and we can look it up and tell you how.
First step is to use the meter to measure the voltage at the battery and write it down. This is important because you can't check the charge voltage at the rear plug if you don't know what your checking against. Next check voltage between the 12 volt power blade and ground blade of the 7 pin trailer connector on the Suburban and see if there is power there. If you find power there, is that power within .2 volts of the battery voltage? If yes, great. If no, not so great.
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If no voltage it's possible that everything is hooked up and you just have a blown fuse.
Try look under the hood on the drivers side by the brake booster of the Suburban. You are looking for a fuse and relay box. Inside that box you are looking for the AUX A or AUX B posts and fuses. See if you can find a wire hooked to one of these posts that goes down and back toward the rear of the Suburban. If so make sure that there is a corresponding fuse plugged in and that the fuse is not blown (ie post AUX A needs an AUX A fuse). If no fuse or a blown fuse put a new fuse in it's place. Now check for battery again at the rear of the Suburban.
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If you can't find a the wire in the relay box, you'll have to hook up a charge wire to one of these posts to charge the trailer while in tow. GM should have left a small wire harness with two disconnected wires behind this box that are for trailer charge and trailer brakes. The challenge is finding those two wires.
If you are lucky you can just look for and spot the wires, they will be folded over and taped to keep the ends clean. On my 1996 the wires are a blue wire and an orange wire. If you can't find them try looking under the dashboard at the trailer brake controller. There should be a wire (probably blue but not always) that goes froward from the brake controller. Try to follow that wire to where it comes out under the hood. Hopefully it goes into the small harness with the second wire.
If you find the second wire you can put a crimp on ring terminal on it and connect it to either Aux A or Aux B, it doesn't matter which you choose. Next make sure that there is a fuse plugged in to the slot that matches the post Aux A or Aux B that you hooked the wire to.
Once the wire is connected you have to find the other end near the trailer plug in the rear of the Suburban. Try tracing all the wires coming off the back of to connector, the wire will be there. Once you find the other end of the wire you can connect it to the trailer plug connector.
Now check again or battery voltage at the rear of the Suburban. If you now have voltage and it's within .2 volts of the battery voltage it's time to move forward.
plug the trailer in to the Suburban and then measure battery voltage at the trailer and write it down. Now start the Suburban and let it idle. Check the battery voltage on the Suburban and the battery voltage on the trailer. If the two battery voltages are within .2 volts of each other and are at least 13.5 volts then you are good to go. If the Suburban battery voltage jumps to 13.5 or more but the trailer battery still displays 12.x volts, then check for a blown fuse on the wore from the battery positive post to the 7 way plug.
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2001 Suburban 4x4. 6.0L, 4.10 3/4 ton **** 2005 Jayco Jay Flight 27BH **** 1986 Coleman Columbia Popup