clocks are wired into the rear lights and by the sound of it theres a crossed wire or two expossed wires touching each over. due the reasons of stealing cars i cant say which wires over ride the ingtion but its very unlike to be on the tail lights end. pull the front an rears seats out and follow the loom from the boot all the way around to the fuse box you will find broken or pinched wires along there.
Thats the cause of your problems.
to help follow the light looms from the bumper not the tail lights there the cause.