Bruce,we keep the downhaul tied to the crew trap as it is the most convenient place for single or double-handing. The downhaul is typically used while going up wind when I'm on the trap. I drape it over my leg in a blow so that I can quickly adjust it. I can't stand it when it is tied to the side-stay because one end is fixed and it is harder to grab in a rush. Matt keeps it on the crew trap even when singling because if it is connected to the skipper's trap it is just one more line to get tangled on when going in or out.
Have fun practicing.
-G