I had a job today that had a balsamoc vinegar spill on white berber. I used stain magic and extracted. it worked pretty well, but what would you use?
If stain magic didn't work and the stain was reddish in color, I would rinse the area extremely well, maybe even with a defoamer, and try Red Relief.
I find that Balsamic vinegar responds best to a good acid-side wine strain treatment. I have even removed it from a wool carpet with no more than 50% solution of white vinegar followed by a plain cold-water rinse.