[Mark44]

If the driver-side and center brake lights are working, it doesn't make sense to swap out the brake light switch. Do you have a wiring diagram for your car? The Bentley service manual is a good source of information for 996 and early 997 cars. If you don't have this resource, there may be wiring diagrams online.

If you have a test light, you can see which wires have power and which ones don't. What I would do is to work back from the non-working brake light and see where there is a dead short. Are you getting power to the brake light socket? If not, go back to whatever junction that feeds all three lights. Somewhere in between there is a wire break.

If you're getting power to the socket, check that the socket has a good ground connection. One thing that can happen with light sockets is that the little spring contacts in the base can flatten out so that they don't make contact with the tips of the bulb. If so, you can sometimes use a pick to pull them up a bit so that they do make contact. I don't recall offhand whether the '04 brake lights have two-filament bulbs.

Hope this is helpful...