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a short in you wiring harness
Check fuses, circuit breakers and wiring harness.
Trailblazer wiring harness for the headlights is a common failure in the early years. HID lights will also cause the same problems if the wiring harness plugs are weak. www.trailvoy.com for all the answers on these trucks!
COmputer, loose battery, defective battery/volt amps or loose wiring harness/ wires grounding out somewhere
Bad relay, bad wiring harness, loose wires or connectors
On my 95 Safari the wiring harness was hanging down and affecting the connection of the low presure switch causing this to happen. Open the hood, look to the left just below the wiring harness. There is a silver evaporator canister with a sensor coming out of it. Run the engine with the air on (watch out where you put your hands around a running engine) move the wiring harness around. If it affect the air conditioning this is your problem. Zip tie the harness to take the weight off of the senor. Good Luck
Run a ground wire to that headlight. If it gets brighter, there is a problem with the ground in the wiring harness.
intermitten problems are the worst to figure out i would first start by changing the bulbs then i would change the wiring harness. i know i had a car that when the tail lights were on the blinkers wouldn't work and it turned out to be a short in the harness.
A friend of mine had a similar problem with an '02 grand prix and it was due to a poor wiring harness that was getting wet.
You might want to check the wiring for the bulb and the harness for the bulb. My bulb would get so hot it kept melting the plastic harness of the bulb. I now have a small stash of extra bulbs. Answeryou might need to change the light or the cord might have a bad connection some were in the wiring
Most taillight problems stem from grounding issues at the back or from poorly executed attempts to do trailer wiring things. If you have a trailer wiring harness wired in and its factory you can easily unplug this at the back due to factory wiring harness plug-ins and see if that makes a difference. I would also suggest replacing all the bulbs (a relatively inexpensive thing to do) because sometimes one bad bulb can cause the wiring system to act irratically. This is most likely caused by a physical wiring problem and not a computer black box related thing.....but you don't mention what year, model etc so its a bit hard to diagnose as is. Good luck !!!!
A short in either the multifunction turn signal switch or a short in the wiring harness going to the switch.