it sounds like a dead short so doubtful relay is causing the issue unless its internally melted itself.
Rear lights shouldn't affect you as its a separate circuit and any issues there should blow the side light fuse.
Look at the plugs/cabling located above the starter motor and under the steering column shaft (RHD) coupling area and of course where the cabling comes out of the large locating nuts on the bottom of the headlight units - all places where cables rub.
