On my "classic" the back of the handbrake switch was been packed with a thick washer to adjust the height of the switch protruding.
I guess mine must be the same, I will take a look.
In 9 years of ownership my handbrake light has worked just once! It came on one evening when I parked up, much to my surprise as I didn't know there was one! The next time I released the handbrake it went off again and I've never seen it since. I'd forgotten all about it until I read this thread.
~iw
