In the steering column there is a circular electronic slide switch that tends to fail on many GM vehicles. It is an expensive part and requires a professional to uninstall/install. It will cost somewhere in the area of $600-$1200 to fix. I replaced the same part in my 1995 Chevrolet Lumina which was having the same problem. My turn signals and back up lights worked but absolutely no brake lights(not even the third brake light). My dad has been a mechanic for almost 30 years and fortunately he had all of the tools I needed to do it myself which saved me $150-$250. Parts for Cadillacs are about 4 times the price of a regular chevrolet. The part for my car cost $150. Good luck and write me back if you find that I was correct with my diagnosis!