I just did this for a bar
sign where I sandblasted the customers logo on the back side of a circular mirror so the logo ended up being frosted glass. He used an LED kit from Amazon where the LED's are on a continuous strip with very high bond tape on the backside. The LED's were attached to the edge around the perimeter so that they were all pointing toward the center. It lit the whole area inside the
sign and looked great. (The customer installed the LED's himself. It takes almost zero talent) It even comes with a remote control to adjust the intensity and color. The kit is already UL approved so you shouldn't have any problem with inspectors. In fact in my area, with LED's being low voltage, as long as I buy UL approved components, the only time an inspector gets involved is when my
sign is connected directly to a 120 volt power supply. nothing to inspect with a plug in the wall unit.
https://www.amazon.com/WenTop-300le...TF8&qid=1518988035&sr=1-5&keywords=led+strips