ignition off - rear lights stay on
 

is it the brake light or parking lights that are staying on? If it is the brake light then check the push button switch that the brake pedal touchs.

Like he said, it's probably the switch at the brake pedal. Had the same problem with mine. Replaced the switch and now its fine. For a temporary fix, just unplug it until you can replace it.
VT247

I had the same problem with my '88. Turns out it was not the switch, but the hole they put on the switch tab to secure the rubber pad (that rotted out) is the exact same size as the plunger on the switch! The plunger was sticking through the hole! I patched the hole by gluing a penny over the hole with JB Weld. It's been two years and all is well.

Hopefully it goes without saying, but you obviously would want to plug it back in before you go driving it. Want to make sure all the other drivers' know you're stopping.

LMAO! You'd hope so! I meant unplug the switch so the brake lights wouldn't stay on all the time draining the battery. Certainly don't drive it without brake lights. Guess it doesn't do much good driving it around with your brake lights on all the time either. Matter of fact, you probably shouldn't drive it until it's fixed.
VT247

ignition off - rear lights stay on
 

Busted Knuckles had the correct repair solution. Replaced a $1 pad - lights went out. Thank you to all that posted a reply.