The existing brake light switch was working but one of the blade terminals was wobbly so I decided to replace it.
A reasonably simple job although you really need to flexible to get up under the dash. I was lucky that the steering column & seat was out of the car which made things a lot easier.
The switch is connected to the brake pedal which in turn is held in place by the brake cylinder push rod. The diagram below shows how it all fits together, although the retaining clip is horizontal on my car.
I added some grease to the retaining clip which made it easier to install. Once installed I connected the two blade connector and the job was done.