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I've just been checking lights on my XJ6 4.2 series 2 1974
When LH indicators are operated the LH rear tail light also illuminates (not flashing)
When RH indicators are operated the RH rear tail light also illuminates along with the number plate lights
Hazard warning work as they should without the rear lights or number plate lights coming on.
I've always assusmed this sort of thing is caused by a dodgy earth somewhere, so have tried running a separate wire from each of the rear lights and the number plate lights back to the battery, but nothing changes.
I've had the car a number of years and all was OK last year when it was MOT tested, and nothing has been changed since then.
Does anyone have any ideas?

It sounds like a classic case of a poor earth. Re-make all connections including the bulb holders.

Now that I've looked at the wiring diagram I realise my error.
Everything works as it should with the ignition turned on!