I have an 82 westie and I had a similar experience.  
     
     One early morning (early enough to need lights) on the way to work I 
     noticed that my dash lights had gone out, 'odd' I thought.  Then I 
     noticed smoke coming out of the light switch.  
     
     I pulled the switch and found the wiper arm (that adjusts dash light 
     level) was discolored and bent, maybe too much heat.  So I bent the 
     arm back and put it back in.  This happened again but this time it was 
     beyond repair.  I picked up another switch from the junk yard and on 
     one other occasion there was a small amount of smoke from the switch 
     but so far it hasn't totally failed.
     
     hope this helps
     
     john

______________________________ Reply Separator _________________________________
Subject: dash lights
Author:  ervolina@watson.ibm.com at NBS-Internet-Gateway
Date:    12/22/95 9:24 AM

On the way to work this morning there was a faint 'pop' and the dash 
lights went dead (the ones that illuminate the dash  when the headlights 
are on).  Fortunately the headlights are ok.  Everything else seems to be 
ok too (including the warning lights inside the dash).  Fuses are ok. 
This is an '87 GL.
     
There are two bulbs (one for the speedo side and one for the tach side) 
right?  If so, its unlikely that both would blow simultaneously.  Is 
there a relay involved that may be the cause?  We're leaving tomorrow 
afternoon for a 400 mile road trip.  Looks like I'll be in the dark ...
     
Tom