Unfortunately, there's no great answer here. What looks perfect on one avatar can look all kinds of wrong on the next. Everyone's got a different shape, so every garment fits a bit differently on every avatar.
Think of it kind of like how tattoos behave in RL. You could draw a square on someone, and as long as they don't move, the lines will be straight. As soon as they change their pose, however, the square won't be really a square anymore.
This is because skin does not behave like cloth. Cloth, for the most part, is fairly rigid. Sure cloth can drape and flex, but in general, garments made of cloth basically hold their own shape, even as they drape over the body. Skin, on the other hand, has no shape of its own. It wraps tightly around the body, and stretches a million different ways as the body moves. Every position the body contorts into causes the skin to reshape itself, distorting its surface texturing in an infinite number of ways.
In SL, there's no such thing as "cloth". Garments are really made of "skin". They bend and reshape according to the size and shape of the avatar they wrap around. They are part of the body, not an external object that simply drapes over it (with the exception of skirts, which don't work very well anyway for other reasons).
For your square, the best you can do is make something that's generally recognizable as a square when placed on a wide range of body shapes. It will never be exact on any body shape other than the specific one for which it was made.
To make a square that fits your avatar's shape, I'd suggest you first upload the templates with the UV lines showing, and wear them. Take a screenshot of your back. Now draw your square over the screenshot, and you'll have a map of how the square fits over the UV's. Pay attention to how the lines of the square relate to the lines of the UV's, and the position of each UV in the screenshot compared to its same position on the template. Use this information to draw a shape on the template that crosses the UV lines at the exact same points that the square crosses them on the screenshot. This new shape will be your counter-distorted square that when distorted by the avatar shape will bend to look like a square.
If you're good with the liquify filter, you may be able to save a little calculation work by simply cutting out the back section from the screenshot and liquifying it to fit precisely over the template. That will show you exactly what the counter-dsitorted square should look like. Depending on what you're doing, sometimes that's an easier way to go.
As an alternative, you might want to get a 3D paint program (Tattoo is free), and use it to paint directly onto the avatar mannequin models. Keep in mind though, that those mannequins have no slider settings applied to them, so while you can certainly paint a perfect square on them, the square will distort to some degree on all customized avatar shapes. Again, there's no perfect solution, unfortunately.
The bottom line is what you're asking about seems like such a simple task in principle, but in practice, it's anything but. Painting straight lines onto an animated 3D organic form is one of the hardest things to do in texturing.
I hope this info helps. Good luck, and have fun with it.
