Yes, under the brake pedal, sort of ....
The link below relates to me changing the brake light switch on my 2005 LR3.
I think the D4 is about the same, ignoring the variations due to the location of the steering wheel. Like all things Land Rover, replacement is easier the second time around, but I can say that very little of my blood was spilled in the learning experience.
DISCO3.CO.UK Photo Gallery - Brake Light Switch Replacement
What does bother me is it sounds like these newer brake switches may not be improved versions but merely just new. Is the switch another one of those pieces to add to the spares kit?
One set of contacts, normally open, the other, normally closed.
Yes, the problem exists even when one does not have ones foot on the brake, actually I think maybe it would not happen if one "rode" the brake.
If you find the stop lamp switch S215 on the pdf below, you will see that while the set of contacts that operates the actual brake light filaments is normally open, the second set of contacts is normally closed and allows signal to the ABS module D277. From there, like Sarah Island, there is no escape.
Also you will note how the Hill Decent relay R222 ties into the tail light circuit so that is why you end up with HDC error messages and Cruise Control not available.
DISCO3.CO.UK Photo Gallery - Brake Light Switch Replacement/Stop Light Lamp Circuit pdf
This will never happen on a Series Rover or a recent Land Cruiser as neither has Hill Decent circuitry. As for Anti Lock brakes, it was never clear that the Series units really needed brakes; for current LC production, Antilock Brakes may still be on the "Available" list of options.