I've just been having this - brake light coming on when I'm on a steep slope or under heavy cornering etc.
Accompanied by a faint but noticeable and slightly annoying scraping noise, normally under braking.
I knew from my last MOT my rear discs were a bit on the thin side, but on checking them was a wee bit surprised to see that my rear pads were very thin. Only a year old too, so they must have been cheap ones!
The pad wear indicator is a wee strip of steel that scrapes on the disc when they are low enough - hence the annoying noise.
When I replaced the rear discs and pads, I found the pistons were very far out indeed. Surprised that one hadn't popped right out.
Simple enough job to do though. Details are in the wiki for
pads and
discs.
Fronts are similar to do.