Here's how I did it:
First I painted a yellow ochre background and let it dry. Over that I laid down burnt sienna with choppy strokes to let the yellow peek through.
Next, I mixed up more color to a flesh-like tone using yellow ocre, red carmine, and white. I painted this mixture quickly over the entire canvas and then, before it dried, sprayed it with water and mopped it off with a wadded paper towel. As you see, some of it came off, rather like an old wall. This is still too blotchy to be a good background, so now I needed to lighten it up.
Next, I mixed up some white with a tiny hint of pink in it and painted this on quickly, sprayed it heavily with water and let it drip off the canvas (onto a waiting towel.) When much of it had dripped off, I patted it with a clean paper towel and let it dry.
I repeated that step two or three times until the whole piece was a few shades lighter.
Finally, I needed to even out the color and lighten the darkest parts so that the blotchy areas would not distract from my subject matter. I painted a soft white into the darkest areas and generally smoothed out the entire canvas with a layer of thinned white. I mopped off any spots which seemed too white. This gave me a white-ish canvas with real depth to the color.
Now these twin canvasses are ready for my next design to be painted on them.