They generally were on a backlight film applied to plexi or glass, but the issue with the colours you see on stuff now though is down to the printing method. To replicate original ones they need to be screen printed, which is applied 1 colour at a time using a pre-mixed ink so the colour is completely solid. Once all colours are screened a layer of white ink is applied over the whole image. When it is turned over the print faces the correct way and the light shining through is a nice solid colour.
I use flexible duratrans film for printing marquees, it's the best material I've been able to get for solvent ink printing. If you find there is too much light coming through you could use a piece of smoked plexi behind it, or a good option is an adhesive paper used for the inside of lamp shades that blocks a lot of light and is heat proof. It's quite expensive though.