So I tossed a hank of pre-washed, recycled white (superwash?) wool in to the liquid and added some (food grade) citric acid. (No exact measuments here, about 2 generous teaspoons.) Could you use vinegar? Absolutely, but I don't care for wool smelling like it, and I had the citric acid around anyways for making bathbombs. Although I did have some alum in the house, I didn't use it. This skein was unmordanted other than the acid.
Notice the great gradiation in color. I started with a homogenous initial liquid. The pot that this was done in however was for the most part unagitated. (No CSTR here.) The orangey-tan bits were closest to the heat source, while the more brick colored bits were closer to the surface. The picture here was after several rinsings in sudsy water. Some of the red came out, but what is there still seems to be fairly permenant. I have read that the red from beets is water soluble though.