What plant?

I made a trellis by bending the end of a remesh panel into a sort of hook to hang over the block wall. It worked very well for cucumbers and tomatos.

You can see it bent over the block wall at the reat. (bad pic, but it's all I found)

Some more vines to consider for Tucson:

One is cross-vine (Anisostichus capreolata) which keeps its leaves year-round, and in spring produces trumpet-shaped blossoms in either a rusty orange or a warm yellow color. If you wall faces north and gets almost no direct sun (or no more than an hour or two in morning), you can grow pinwheel jasmine (sometimes sold as confederate jasmine; proper names is

Trachelospermum jasminoides), with rich-green foliage all year and intoxicating sweet white blossoms in spring. Both these are frost tolerant. A trickier vine here is lilac vine (Hardenbergia), that keeps its slim leaves all year, and produces little racemes of purple flowers very early in spring, but needs to be covered in frost.

A woody semi-vine that tolerates blistering sun is firethorn (pyracantha). Shoots that come forward can be snipped occasionally to keep it relatively flat. It has deep green glossy leaves year round, cream colored blossoms in spring, and clusters of gorgeous orange or scarlet berries in autumn and winter.

Don't plant anything until late September when temperatures cool down. That will new give plants autumn and spring to settle in and establish their roots before the onslaught of next summer's heat.

Good luck finding the plant that is right for your situation!

I did the same as this article and used store displays for my vines. It adds some architectural feature to the wall and I don't have to worry about the wood rotting. I found some used displays at a store display store in Phoenix and saved a bit of money (you do need a hammer drill for block wall). The only problem I have had is that I planted Lilac Vine and it has taken forever for them to grow. I don't know if it is the location (not a ton of light) or watering. I have also wondered if I should have amended the soil a lot more as I think that right next to block/stucco wall there is construction debris in the soil.

https://www.gardenista.com/posts/diy-instant-trellis-made-from-commercial-components/

I would check out Cat's Claw vines! They're considered invasive in many parts, but I personally prefer the term hardy. They love hot walls, full sun and reflected heat. They will climb up anything and everything, VERY quickly!