Answer: My first thought is that the soil will likely be made alkaline, thanks to the lime in the concrete deck and retaining wall. You can purchase a pH test kit at any garden center and do a quick reading to see if you need to adjust pH for the plant you eventually choose, since most plants don't do well at pH greater than 7.5. Also, to get established, any plant you install will need supplemental moisture for at least a couple of months, and perhaps all summer the first year.
Chameleon Houttuynia doesn't climb, but it spreads rapidly. It's coloration would be most dramatic in full sun, but it will grow fine in partial shade. It does prefer moist soil. You can reduce watering needs by mixing water-holding polymer, like Burpee's Terra Sorb, into the soil at planting time. Use it as directed on the label -- if you use too much or put it in the wrong place you can end up with a mess as the crystals engorge water.
Groundcovers more tolerant of dry conditions once they are established include ornamental grasses, dwarf daylilies, and pachysandra. I hope this helps!
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