I am not sure what could be causing your problem. I went through something like this and I ended up solving it... but I don't really know why. In any case, if not for solving purposes, here's my story at least for entertainment:
I was replacing the rear brake lever because I somehow bent the tip. I took my time and as I put everything back together, I found that the brake light was permanently on, regardless of whether any brake was applied or not.
I took it all apart again and as I put it back together again, I put some grease on the pin that actuates the rear brake. I finished getting it back together, and the problem was gone.
It's worth noting that even before I disassembled again and added grease, the pin was correctly moving and engaging/disengaging the rear brake, but the light was constantly on. Once I put grease on it the second time, there was no clear difference on applying the brake, but the light was no longer constantly on.