I had this same problem on my 2012 RX450H. it happened after i changed my rear side light bulb and straight after changing my LED brake stopped working. It would have cost me around £500 to change the the rear light unit. Had to be a better way.
After checking power coming to to circuit being ok i was baffled. I checked online and found other people in the situation after change rear side light bulb. My mechanic finally found out what the problem was. When you change the rear side light bulb you can very easily snap a very fine and tiny wire connector that connects to to brake led light circuit. It is very hard to find but a good car electrician will find it. My mechanic, who is a friend of mine, just re soldered the connector and, hey presto, my brake light was working. Whats more he did not charge me.
I was so relieved and happy.
Hope this inf helps others.
Jack
