When I start the engine, the tail light works (but not the brake light).
The second suggestion sounds more plausible but I don't really see the switch assembly you are talking about. On the left brake lever, I don't really hear a click. For the right one, I here a click and see that the brake lever depresses this little button that is clicking. The left side is a completely different configuration and there is no little button (because it is completely different, no space for it or its hidden). If one side is clicking it, would the brake light come on? Or does it require both sides? What else should I check?
Thanks for your help and suggestions!!