I can't comment on the detils of your vehicle specifically, but generally the positive wire to illuminate a radio display (I assume this is what you mean by "radio light") is wired into a switched circuit so that the radio only illuminates under certain conditions such as the ignition keyswitch being on, in the accessory position, or the vehicles lights are on. It may be that this radio is not the original, and someone has installed it incorrectly by connecting the wire to a positive that is permanent.