I grow azaleas for their flowers and am not focussed on trying to make trunks with them. I find them to be slow to thicken even though the principle is the same as with any (temperate) tree: lots of foliage on a stick is the way you make it thick.
So, if you want to have a trunk, prune off the branches from the base, leaving only the one stick you want to become a trunk. Then you want to encourage all the foliage growth on that stick that you can get. Most azaleas readily back bud, some are so much so that all you need to do is expose the bare stem(s) to sunlight.
I shear and deadhead my azaleas after they have bloomed (they begin growing vigorously at the time they bloom) and again about August (February for you, I believe) which does stimulate backbudding. You may want to remove the flower buds as soon as they are set so that all the plant's energy goes into vegetative growth. Some evergreen azaleas set flower buds in the fall, others in the spring, but regardless, they are always at the tip of a twig, so this can usualy be done by trimming/shearing at the right time instead of tediously picking each bud one at a time.
In other words, if you are after just making a trunk, shear it in the spring, put it in the sun, fertilize, water, and let it grow.
Again, I grow azaleas for their flowers. I shear them at least twice a year. My focus, though, is on sculpting the canopy where the flowers will appear. For me the skeleton is secondary. Over time, I clean up the stems and even remove some to make an attractive skeleton.
so to thicken anything it has to grow longer. Simple as that. That may take forever depending on how slow it grows.
