Do you have a 4 way plug at the rear of the Trailblazer,(1 ground and 3 hot)? Check that with the tester, pin 1 is signal/brake right, pin 2 is signal brake left, pin 3 is park/running lamps. If you have a left signal flashes with the brakes and right signal on, then you are most likely right, bad ground. Pull the bulbs out, clean the inside of the sockets with an eraser tip, clean the bulb bases and contacts and then grease with vaseline. I'll bet that 99% of trailer light faults are ground issues. Personally, I run a dedicated ground wire to each of the lamp bases, soldered and liquid taped, no more problems.