I had to figure out my zinc deficiency alone. But when my vision in my left eye sharpened when I took it and blurred when I didn't, I figured it out pretty quickly.
I use 30-50mg of zinc picolinate to rebuild, and I'm careful not to deplete my copper. But that shouldn't be a problem unless you are supplementing for over a month or already low in copper. I wish I could give you a good test for these nutrients, but I can't. I often refer to acu-cell.com for info on minerals and it has proven very helpful.
You may be able to replenish your zinc a bit faster if you also supplement magnesium and B2. B2 improves magnesium absorption, and apparently magnesium and zinc often reflect each other, perhaps due to similar metabolic pathways in the body. This is also mentioned under calcium/magnesium at the acu-cell site.