Mur's probably right about the fuse but the wiring diagram for Mini 1000 with triple gauges 1976 onwards in the Haynes manual shows a fuse on the brown wire. Intermittent electrical problems are a huge PITA.

Well, I've been also having some issues with the turn signal switch so I have both on order.  Now I have to learn how to do the relays.  Problem with these types of things is you do it so infrequently that you can't remember and have to relearn :(. 

There is no fuse on the brown wire.

It is +12V straight from the main post on the solenoid. The red wire heads off to the park lights after going through either an in line fuse or the lower fuse of the MK IV onward fuse box.

The blue wire heads off to the headlamp dip switch, which often fails as well, and then continues as either blue with white or blue with red to the high and low beams.

Sorting this out generally requires both switches; the headlamps switch and the multi function turn signal dip switch, AND fitting a pair of relays to carry the actual current to the lights. Done right you will never have a problem again.

You can use the board's search function to see how some folks have done this, or sort through many links and videos if you look on google. The big thing about this problem is that sorting it out correctly will cause you to learn pretty much all there is to know about wiring in cars that aren't over controlled by central computer systems.

The brown wire is the hot one. The blue and red should have 0v with the switch off and 12v with the switch on. There is a fuse on the brown wire maybe its burned out or intermittent.

The head lights should be on a relay. That switch is at it's limit doing lights. Buy a new one and plug it in. Be careful if you pull the switch out of switch plate the lower pin may be hot and can short to switch plate. There is another problem with the plug it's white plastic and if the pin bores are black they have been arcing and this converts the plastic to a conductor and you get a hot to the touch plug. I'd suggest you get the plug and switch if you drive at night or with lights on. I'm thinking about running my grille lamps all the time. People are not paying attention. Steve (CTR)

My headlights worked intermittently and now have stopped working all together.  I'm suspecting the switch.  It is a rocker switch with 3 pins, which connect to blue, red, and brown wires.  I'm trying to figure out an easy way to test if it is the switch without waiting a week and $20 to get a replacement.  Does anyone know how the wires are connected in the on and off positions?  I can then just jumper the wires to see if the lights come on.   I tried looking at the car wiring diagram and it's not clear how the switch connects the wires in on and off conditions.