I've never read about anyone doing it on this or any other board. Maybe someone has, but I don't know of it.
Back in the days that I did coffee packaging, we used a 5 color process that involved transfer, not printing. So basically it was kind of like a film heat transferred. CMYK+white. So... all of the colors, then the whole thing was covered with white to make the colors vibrant and as opaque as possible. Reverse printing is tough, which is why we did transfer, reverse painting is even more difficult.
I wouldn't paint a marquee reverse or otherwise. Printing looks so good, and marquee printing is about as cheap as it gets in this hobby. But i'm not that into painting.
If I WERE going to do it, I'd probably use Acrylic artists paint, as it's easy to work, dries VERY fast, and easy to mix. When I did more painting I used to use Liquitex Acrylics for painting rather than craft paint, as craft paint is much lower quality and less consistent. I would use about 10 tubes of paint and that was enough to mix pretty much every color. Where possible, I used very opaque colors, except for the extreme colors like deep blues, purples and greens where you gotta get vivid colors and mix in white to make them opaque (where needed).
Opaque
1 titanium white
1 mars black
1 cadmium red
1 yellow medium azo
1 cyan
1 permanent green light
Translucent
Phthalocyanine Green
Dioxazine Purple (no matter what they say you can't mix purple... so get a tube or purple... green's almost as bad)
Cerulean blue
can't remember the rest of the names... but it was a cool yellow, a very cool (and expensive) blue, a cool red/magenta
Acrylic could work fine on glass or plexi, but it would be challenging to get it the right thickness as a glob will show when a light passes through it. A hair dryer works great with acrylic, so you can get different sections to dry very fast if you work thin. Mix small amounts of paint on paper/styro plates as you need. Spray lightly with water to keep the paint workable on the plates (if you want)
You can trace over an existing image, by putting it underneath your plexi and sliding a piece of tracing paper between it and the glass (to make it easier to see what you're doing versus what's there already). If you do this, remember to flip the image. Start with the detail/linework first, then add the fill-in colors. Finally you can coat the whole thing with white to keep the light from being to intense.
that said I wouldn't do it.