Although it was the radio which first brought this to your attention, I'd forget about the radio for the moment and start looking for a short-circuit at the rear of the vehicle. I think there's a short-circuit between the 12V feed to one or more of the rear lights, and the chassis. Unfortunately I don't have a wiring diagram, but apparently the rear lights and dash lights share the same fuse ( I gleaned that info from reading some old threads here on the forum).
I'd make a close visual inspection of the wiring harness back at the rear lights, paying special attention to any points where it enters/exits the bodywork via rubber grommets, and also any flexible sections, such as the flexible conduit running from the main bodywork to the tailgate/trunk lid. I'd also inspect the rear light clusters and connectors, looking for dampness and corrosion, which could cause a short-circuit path.
Finally, have you replaced any rear light bulbs recently? Apparently, you can get bizarre fault symptoms if a single-filament bulb is inadvertently fitted instead of a dual-filament - see the following thread, especially post # 7 onwards:
http://www.automotiveforums.com/vbul...d.php?t=577335
I'm fairly sure that your problem is a short-circuit though, and although it could be up front in the vicinity of the dash, I think the rear of the vehicle is more likely, because the wiring back there is more exposed to chafing and bumps and dampness.