Tail light stays on

Thats a good one, I have been puzzling over it for a time.   I would re-post your question framing it  "P11 desert lead bike tail light stays on"   ,we have some  P11 experts that may not have noticed . That should spark them up!

I recently had a similar problem. Found it was not the taillight but the brake light that was on. Adjusting brake light switch position solved it. So before replacing the light switch, which is the most likely culprit, check which filament is glowing. But after half a century of seeing the most abominable modifications of vehicle electrics made both by professional and backyard mechanics, I do't rule out anything.

.. most likely tail light - at least the switch - the leads to the tail & stop light may have been crossed over so the switch operates the tail light.

When resuscitating my Dommie earlier this year , I had, what I thought was, a similar issue. 'Tail light' was always on, got bright when pressing the brake pedal so not the brake light? Wrong! The brake light switch had partially melted and was acting as a resistor in the brake light circuit.  Pressing the pedal bypassed this resistor giving a bright light. New brake switch (now on front brake lever) cured the problem and lights work as they should.

Regards, George. 

... of course mean brake light in my post above. Added to which it's not unknown for people to force double filament bulbs in the wrong way (for those few who don't know the bayonet pins are offset).

I thought the Yanks adopted always on lights at that period. I agree about melted switches and bodges to wiring looms. I now try to adopt anything that fits off of current Motorcycles. It makes it cheaper if one has a whoopsie to get off of ebay.

There should not be a relay in the system so.....

If the taillight was off before you switched on, then wouldn't switch off, I am guessing that a set of contacts are stuck (melted?) together.