....as it should!
Up here in the icy north the days are getting longer. Some seem really long when one is pining for a Mini drive. C'mon April!

Getting close to putting the Mini away for the winter.  My other old cars are buttoned up but as long as I still have a few dry days I'll keep the Mini out.  If nothing else it gets twice the mileage compared to the others.

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Advantages of the incremental model By using the incremental model in the development of a project for which it is sufficiently suitable, one can be convinced of the following advantages: the customer has the opportunity to comment on each developed version of the system, more info here; the divide and conquer rule allows you to break the problem into manageable parts, thereby preventing the formation of cumbersome lists of requirements put forward to the development team;  

Yaaaaay!

Well the nice thing about being retired with some old cars to play with in the garage is - When I run out of ideas for WHY it's doing that, I just go back in the house and say "tomorrow or the next day".

First I thought the problem was in the steering column where the high/low beam switch is, I even bought a new assembly from our host.  Nope that wasn't it.  Since I replaced the stock headlites with ones from a Jeep, they have a circular lite that I added blue bulbs for driving lights, that was the other end of the issue.  Nope not there either.  So with Dan's help it was following wires.  I have 4 wiring diagrams and none showed a relay that the headlites go thru.  Tracing the wires back from the headlites I found it.  Simple just a wire came off one of those relays.  Now I'm back in business again.

Hope you aren't getting fire-hosed like BC did.

Thanks Dan, It's a 1993 determined by the plate on the truck latch.  I purchased it from Calif so you know what that means about the VIN.

Today I'm going to crawl in upside down under the dash and try to follow wires based on my wiring diagram.  I'll figure it out sooner or later.  The wx here in Oregon has been blowing 30mph and pouring down rain all nite and will continue for the next few days so I'm not going outside anyway.

I don't see where you indicate what year your Mini is or what market it was made for - UK. continental Europe, Japan, other?

Before 1988, the lights are switched as described.
From 1988 on, things are different. A "dim/dip relay" was added. I have no idea where it is or what it looks like. It should have 7 wires coming out of it
- green (from a fuse 1-2 in fuse block, controlled by the ignition switch)
- blue (from light switch)
- brown/orange trace (from fuse #19, an in-line fuse and through the "dim/dip" resistor, mentioned by 6464s)
- blue/brown trace (from headlight dim switch)
 - blue/red ( goes to headlight dip (low beam) lights.
- red wire to fuse 7/8 in fuse block)
- black ground wire.

I have no idea how it works, but it was probably added to take the current load off the light switches.
According to Haynes wiring diagram 18, the high beams appear to receive power from the lighting switch, not the relay.

The wire connection where it splits to go to each headlight, should be tucked up inside the bonnet slam panel. There is a biggish loom bundle that leads to an assortment of things like the alternator, ignition, temperature sensor etc. The headlight wiring is likely tucked in behind it. It has to split somewhere...

Dan thanks again for your directions.  

However I'm still not getting any lites.  Everything is good thru the steering column with the old turn signal/headlite wiring and a brand new one.  After that I'm not sure.  I found a red/blue wire on the grill but it comes out and is jumped to a relay above the solenoid that doesn't have anything to do with the low beams.  Also couldn't find any one into two connector that would split and go to the headlites.
 All the other lites are normal, High beams, high beam flasher and the driving lights.

Getting cold in my garage so I'll go back and mess with it some more tomorrow.

Thanks Dan.  Yesterday I was trying to check the fuse on the two inline fuses I have next to the fuse box.  Devil of a time trying to open one and I may have wrecked it and of course the fuse I wanted to check fell in behind the engine, which I couldn't find.  Sooo I'll fix or replace the inline fuse holder and go back and follow your directions.

Thanks will see what today brings.

KO

Dan, Great explanation to the headlight wiring. I do want to add that some late model minis, mine being a 1994, have a fusible link.

Assuming your car has an alternator and not a dynamo (generator) with a voltage regulator:
Power from the solenoid battery terminal goes up one of the brown wires to the hot side of a fuse in the fuse-box.
From the same terminal, a brown wire goes to the lighting switch (in the dash).
From the dash switch, a blue wire takes power to the "indicator switch" (on the steering column) which houses the high/low switch, passing through a multi-connector.
From the high/low switch, two wires lead to the headlights: blue/red trace to "dip" beam aka low beam and blue/white trace to "main" aka high beam.
There should be no fuses in the circuit.
If you are getting high beams to light up - then you are getting power to the column switch. Your problem may lie in the blue/red trace wire or its several connections. I would start where it has a one-to-two bullet connector behind the grille where the power splits to go to each headlamp.

Cars with a dynamo and voltage regulator are a little different. from the solenoid battery terminal a brown wire goes to the "A" terminal on the voltage regulator. From the "A1" terminal, a brown/blue trace wire goes to the dash lighting switch. The rest should be the same. (I seem to recall the "A" and "A1" terminals are directly connected inside the regulator.)

Check the big brown wire on the solenoid, they furr up and you lose permanent live for the headlamps.

Got ready to go out with a return after dark and checked the headlites.  Nothing.  Pulled the headlites and checked the wiring, OK, then checked the wires behind the switch, OK, then pulled the cover over the steering column and wiring looks, OK, but there's no power to the side of the switch that goes to the low beams, the high beams and high beam flash are, OK.  The fuse panel on the firewall with 4 fuses are, OK.  Sooo I'll start looking for and inline fuse somewhere.  

Anyone have  a similar problem??