1. Fuses. Duh. Go ahead and replace any of them that appear to be blown.
2. Replace the bulbs. Go ahead and replace both of them with a fresh bulb. The brightness will match with each other, etc. and you dont have to worry about them burning out anytime soon again. This could very well fix it. One time, one bulb filiment broke, (blew) but it landed on the other lead, so the bulb was still working, but when I hit bumps or something, the filiment would shake off and sometimes it'd shake back on. That was puzzeling to me for about a week
You don't need OEM BMW lights, NAPA's got them, I'm sure other places have them too. It's cheeper that way. A light bulb is a light bulb.
3. Replace the brake light switch. It's under the dash, hooked to a bracket infront of the brake pedal arm. DO NOT buy the switch from bavarian autosport, it's VERY LOUD and makes an AWFUL clicking noise... I even tried disassembling it to fix the noise and wound up breaking it even more. Go to the dealership and get the brake switch.
There are 2 kinds of brake switches, 2 pin, and 4 pin. If you have cruise control, you have the 4 pin. You can see if you take the leg panel (under the steering wheel) off with the 3 screws. 2 screws facing the front of the car on either sides of the steering wheel, and 1 screw facing up on the underside, close to the transmission. Unhook the vanity light and the "Bing" speaker and put the thing aside. Go ahead and take it off to identify if you have the 4 pin (it's got 4 wires going to it) or the 2 pin (it's got 2 wires going to it). Go to a dealership or call them and order the E36 (2 or 4)-pin brake light swithch.... Bimmerparts... Wherever, just get an OEM switch and not an aftermarket one, then you wont have a loud ass clicky one that you throw away cause it sucks and was a waste of 30$
If it's neither of those 3, then you have a wiring fault. That's bad. It could be anywhere.