A bad T/S is a common problem. Both brake lights must go through the T/S switch. While stepping on the brake pedal, try wiggling the T/S lever and see if it comes on.
do you have more info in the T/S switch diagnose, removal and install. As well as the source of the best quality T/S switches available?
I read that the break signal also goes through the lights switch, is this so?, could I check something in there?.
For what I saw with the multimiter there was only one line with 12V when I step on the brake at the connector behind the kick panel, at that location there should be already 2 lines with 12V, or the brake signal is split after that connector?