My guess. it is just the barrel plugs. as they   turn green with curd..  little vasoline  will eat it off.. along with some help of small wire brush.. later bvc

Sounds like you have a relay sticking causing it to be on for no reason.

Check to see if any of your electrical components have the word LUCAS stamped on them. That would be the main problem.

What are the answers to my other questions?

Yes just the left. everything else works normal

What year is your Mini?

Is the problem with just the one headlight?  
What happens when you turn on the low beams?  Are both on as expected?
What happens when you turn on the high beams?  Are both on as expected?

My left headlight came on in the night and wont go out. I found going up a steep driveway fixed it for a minute but going down turned it on again. Then it went off driving and came on again when I stopped ?????????????????

Thank you very much.  I will read the article after work tonight

Jack

OK, I have written this out several times and I think our hosts are sitting on an article that details your issue.  It would be nice to just post a link.

In any case.

The car does not have relays.  The headlamps are not fused.  The headlamps switch is weak, and so is the dimmer/signal switch.  They fail.  They fail one after the other, and the wires leading to the headlamps switch can fail, and that plug can melt, and I have experience where someone completely gave up on a car because this issue was not addressed.

If you can poke about with a test lamp you can fix this stuff.

First.  lan on fitting a pair of relays to carry the actual current to the headlights after you have sorted out the issues at hand.

Now, each headlamp has a sub harness and these wires meet nearly in the middle of the slam panel, where the hood latches, at the front end of the wiring harness.  The connect in multi bullet connectors, and these can come undone.  Check all of those and check the ground one as well, and check the battery grounds and the engine to chassis ground and the wiring harness main ground.

remove the headlamps switch.  If it has tried to power halogen lights for about a year it is likely overheated.  Check the plug behind it and the wires therein.  You will want a new switch for sure, as well as any wires to be repaired.

The dimmer switch/turnsignal is a wear item.  Your issue sounds like it may be just in the switch, but I am not looking directly at the car so that is mere speculation.  When you FLASH the high beams by pulling the stalk back, you are actually powering them via the horn circuit.  This is a tiny power source and will likely find grief at the amount of load if you do this a lot.  Note that once you fit relays, this won't matter.

If the headlamps switch is fine, the dimmer is fine, and the wiring up front is fine, then the lights will work again.  Adding relays simply gives a new, heavy duty, source of 12V DC for the headlamps, and the relays are triggered by those wires that used to feed the headlamps.

Once relays are added, the headlamps switch only carries current for the park lamps and the dash lights, and triggering those relays.

Turn signals get their power via the hazard switch:

//www.minimania.com/article/3124/MK_III_Turn_Signals_and_Hazard_Switches

Here is a good read on what goes on there.

Greetings all I new to our classic minis.  I did own a 2003 modern one for several years.  As of last week I own a 1987 classic.  Head lights were working fine then the next day the low beams would not come on, the high beams worked then later I could not get them to come on except when the lights are flashed.  I also note that the turn signals work but there is no "blinking" sound.  Since the lights will come on when the stem is pulled back but not when in the low beam or high beam setting I wonder if the problem is in the signal stem itself?....relays....fuses....  On a smaller scale I my cabin ligh also does not work.  Im n mechanic nor electrician but I tested the wires and 1 of the 3 had power and the bulb would light if I made contact with the light tester.  I fear what Ive gotte myself into....lol  Thanks, Jack