Look at #8 on this diagram-- that's usually the problem in situations like this as it's easily damaged-- especially if someone replaced the brake lever without following the instructions in the manual. If the shim (#6) is missing or not in the right position, that could cause your problem as well.
It's sort of a bugger to replace-- not hard, just fiddly and not much room to solder, and getting it to sit right can be an exercise in frustration.
The part can be found aftermarket cheaper if you do some hunting.
Item #6 is actually a spring clip. it is real small and can be overlooked. It holds the brake light switch (#8) firmly in place so it does not flop around.
#6 is easily overlooked or discarded when dismantling the right control and can be dropped without noticing it when replacing the switch.
The brake lever pushes on the switch button until you apply the brakes. This releases the button and the brakes light. If this spring clip is not properly in place the brake light switch is flopping around and the lever can not hold it compressed.