It sounds like a simple enough of a design. LEDs are very low temperature so you can build them into any enclosure. Mounting the glass is less of an electrical issue than the glass issue. It would seem to depend on what the nature of your glass is.

Actually you'll likely find some help by going to a picture framer. That's the kind of thing they get into.

Light box with a couple florescent tubes on each side running vertical with the front of the tubes obscured by the 'frame'.

Paint the back of the box the whitest flat white you can find.

A daylight color tube often looks best, but you may want to try other CRI tubes depending on the colors in the glass panel.

A daylight and a couple incandescent bulbs will make a very accurate 'daylight'.'
This combination was used for many years to judge color balance in photography.

A daylight and a couple incandescent bulbs will make a very accurate 'daylight'.'

I never thought any daylight lamp looked much like any "daylight" I had seen. Now I know why...

Unlike the sun, or an incandescent bulb, florescent tubes produce spectral lines at only a few colors.

The spectrum of the sun and incandescent bulbs is continuous with light from infrared up to a peak (and then a roll off) based on the object absolute temperature (black body radiation).

Discharge lighting has even fewer spectral lines.

At least with florescent additional phosphors can be added to create more colors in the light produced.