Hiya
The dim dip resistor and relay was added into the mini wiring loom in the 80's, it was in anticipation of a change to the Road traffic lighting regulations which never actually came into affect...
What it does is when your side lights are on and the ignition, the headlights are also switched on automatically by the relay (this is the big pink thing behind the dash ). The resistor (the brass thing on the n/s end of the bulkhead ) is used to 'dim' the headlights in this condition so they are not on full power at start up.
Oz Cooper
Classic Mini Guru UK