While searching for LED sign bases for edge lit acrylic signs, I came across an item that made me think of this. I have not done it but it should work and is easy to implement.
Carve or 3D print a base that can accommodate tealight with a slot to hold the acrylic. They make flickerless lights that can be used.They even come in different colors. Remove the faux flame and voilà! instant edge lit sign. No wiring needed!
I suspect that method may be a little dim, maybe not.
Worth a try but batteries are a PIA with these. I prefer lights with power supply or USB.
There should be a cheaper method somewhere that is pre-wired with bright LEDs.
you could use LEDs, a lipo cell and an adafruit powerboost to charge it. Pretty low cost and wireless. Lipo can be chosen according to your size and power needs.
The HD link has the cost at 90 cents each tealight. I agree that batteries are PITA but for a quick project and next to no assembly required, not a bad deal.
I designed and carved my own frames out of mdf.
Is that two halves with a partial channel and then glued together?
I decided to try it out. I did the whole project in about half an hour on my laser. It is rough but proof of concept.
I apologize in advance for the quality of pics.