It will only support itself on very rough surfaces and in the case of brick or stone walls, that is usually the mortar joints. I had heard stories of it climbing up to the top of brick chimneys, so I planted mine adjacent to a brick-faced retaining wall and trained it to grow upright with the aid of a temporary wooden "ladder". It promptly began to expand and grow lateral branches, which attached themselves to the mortar joints. After a few years it became very large, with lush foliage. Two years ago, during a brief, but very heavy, summer rainstorm, the entire vine came down. The weight of the moisture on the foliage was just too great for the roots to support.
You will probably need to support it by using "concrete or mortar" nails, driven partway into the mortar joints and a dark colored plastic twine to attach the branches to those.
That is how landscapers train woody plants when they are espaliered against a wall. If you have a dry-set stone wall(no mortar joints), use any type of galvanized nail that can be tightly wedged into the joints.
Good luck!

Thanks so much for the instructions! I will go examine my wall and see what I can rig up.