Since etching is creating microscopic surface height changes my immediate idea is:

1. place point light source at very sharp angle, maybe a laser
2. use dark background, maybe a flocking paper
3. paint the facets black to not let any unneeded light into the glass from the sides

I imagine it will create visible outline of the etching. Maybe shining the light through the edges (and not letting it through the top) will work better. Maybe you can paint the etching white with some chemical (so that the paint fill the carves tightly) and then shine the light through the edges, that might work too.

Another suggestion is to maybe make a sandwich of clear glass + coloured solution + slide and squeeze it (slightly). I imagine it would leave small amount of solution where material was etched. The solution must have very low viscosity I guess.

If you use a coloured solution and cover it not with clear glass but with something bendable (maybe thin plastic or even plastic film) I imagine you can get an outline too since small amounts of solution will be trapped where the sharp height difference is.

I do not know what the etching depth is but if nothing works well there's also interference light tricks that you can explore. The principle is that self-interference of light can reveal the etching because it depends on the optical length.