Hi Rod,
I'm not sure what you've actually got. Is it one of the lacquers for RC bodies? If that's the case I'm not sure if it's suitable for use on styrene, as these are formulated for use on polycarbonate. I would expect that if applied thinly in multiple coats it wouldn't have any detrimental effect on the styrene.
BUT: The R/C paints are meant to be applied on the inside of the R/C bodyshells and the gloss is imparted by the shell itself. In my experience with R/C paints, typically they have an eggshell finish and are not glossy when dry.