Not everyone got that feature from the manufacturer. Do you have the original radio installed? If there is or was an aftermarket radio in there, I'd start by looking at the wiring harness. The radio has a switched 12 volt feed to turn it off when the ignition switch is off, and it has two wires for the display. One comes from the tail lights to tell the display to dim, and one comes from the dash lights to tell it how much to dim. Sounds like one of those display wires may be touching a power wire. There's also a 12 volt memory feed wire to the radio. That circuit is always tied in with some other circuit that is always live. That could be the horn, the brake lights, or more commonly, the cigarette lighter.