2001 Chevy Trailblazer Brake and backup lights

My lights turn on when I switch on my lights for night time driving. However, when I depress the brake pedal, only the high center mounted brake light comes on. Also, when I shift into reverse, my backup lights do not come on. I have replaced the bulbs and checked the fuses. I was told that the stored wires for a trailer hookup could be shorting out. I checked those fuses and pulled the wires on the stored bundle to check for broken or crossed wires. Did not see any noticeable signs of a problem. I rewrapped them and tucked them back into place. I'm am now at a loss for what to do or where to look. I'm kind of hoping to avoid going to an electrical repair shop for something that may be an easy or economical fix.