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
On "classics" they are also earthed at the switch but as the switch is plastic there is a fly earth lead. Could be this. You'll find (if like mine) the washer is "trimmed" so that it fits against the side of the handbrake housing.
They are held in place by a nut so this may have also come loose. The nut does not come with a replacement switch so keep this safe.
The part you need is Lucas SMB421 and is easily available on eBay for much less than the dealers. With postage about GBP7.
It's fiddly to do from underneath without removing anything but quite doable. If testing with a multi-metre remember it is normally closed and push to open.
