As
@Redcoat once wrote to me, credit where credit is due.
The rear light. On close inspection the bulb had been inserted incorrectly - as you know it's an off-set bayonet attachment. An some point in the past the bulb had been fitted with the bayonets in the wrong side, creating an ineffective circuit, which worked sometimes and not at others. The bulb was forced so strongly that a new channel was scored on the inside, making it hard to see the poor and erroneous fitting.
When I unscrewed the fitting in the workshop on Monday the bulb was blown - black and the edge of the plastic distorted from heat! Is it possible that this little perisher has caused the lights-on - lights-off issue? Either way, the rear lights, brakes included, now function as they should.