The vinegar will continue to thicken when you take it off the heat, so do not keep on cooking to the syrup stage. Take care to remove also because the vinegar will acquire a burnt taste.

Do you mean reduced balsamic vinegar? You simply put balsamic vinegar on the stove top over medium heat. It will thicken gradually. It becomes thick and sweet tasting. At this point-if you wanted to do a dressing, you could just drizzle a salad with olive oil, perhaps a bit of salt and pepper, and then top with some of the reduction, I would think.