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I would check the running lights for one with a short. I had the same sort of thing with my trailer and I spent way to much time troubleshooting the brake and signal wires. Turns out a running light bulb connector was grounding out on the trailer and messing it all up.
Vehicle side, Brown, running lights Yellow, left signal/brake light Green, right signal/brake light Black, ground Trailer side, white is ground
They are lights that go on your trailer to show your turn signal and brake lights. Reese Hitches has all of the top brands if you're in the market for some: http://www.reesehitches.com/product_categories/trailer_lights
Short circuit , maybe ????
If you have the same bulb for brake and signal, brake light power needs to be interrupted by the signal lights, The brake circuit has to go through the signal light switch so the problem could be there.
the turn signal switch is probably bad
Assuming the signal lights still work, no. But a bad brake light switch or a blown brake light fuse could.
Your trailer tailights are dual-filament, with one being the running lights and the other the brake lights. You need a separate power source from your towing vehicle's brake lights to power them. The easiest way to do this is go to U-Haul and but a set of their trailer towing taillight bulbs for your towing vehicle. The bulbs replace your standard tail/brake light bulbs, and they have two wires coming out of the base of the bulb. One of the wires connects to your trailer's running lights, and the other one connects to your trailer's brake light circuit. I'm trusting that when you re-wired your trailer, you ran two wires from the taillight socket, one for the running lights and one for the brake lights. In some trailers, the brake light circuit also doubles as your turn signals. Good Luck.
short circuit on trailer light wiring
Check the brake light fuse, the bulbs, the brake light switch and last, check the signal switch.
At the right rear light the brake light wire is white. There is a manufacturer installed connector for a trailer lighting kit use located about 12 inches ahead of the left rear tail light behind the plastic panel holding the accessories options. The connector holds an orange wire for continuous power. It also has the white wire for brake lights. It has the dark green for right signal lights, yellow for left signal. At the right rear signal light assembly there is more than one dark green wire.
If the Avalanche came with the factory trailering package, the trailer lights are separately fused from the other truck lights. Check your fuse panel layout for a 10-amp fuse for left side and a separate fuse for right side turn signal/brake light on the trailer.