If both your tail light and brake light aren't working, check the bulb. They do tend to blow relatively easily. If it's just your brake light that isn't working, check the intensity of your tail light. If it looks brighter than it should, your brake light switch is likely stuck on. (This is assuming you have a rear coaster brake and not a drum). A stuck switch can be checked by removing the brake light switch actuator (a fancy name for the wire running from the coaster brake arm to the switch). If the intensity of the light is lower once that wire is removed, then you have found your problem.
Assuming that is the problem, you will want to look at the brake arm retainer (the black thing with four allen bolts). If the arm is binding tightly on either side of the slots in the retainer, loosen the four allen bolts that hold the brake arm retainer and slide it off the arm. You will need to remove the return spring first. Turn the retainer around and slide it back on the arm, reinstall the four bolts and check to see if it's binding. Hopefully it won't be. Make sure everything is tightened well and reinstall the spring and the wire actuator.
My brake light wasn't working (or so I thought) on my Whizzer, and turning that retainer around is what fixed the problem. It turned out that the brake light was on all the time before I turned the retainer around.
I hope this is of some help.
You know what? I went out before I wrote my entry, and turned on the key. all the lights went on, then I disconnected the fuse, and all the lights went off. I did NOT however start the engine, so it seems I might have gotten it wrong. I did have to replace the fuse some time back, but I can't remember exactly what the symptoms were. The headlight wasn't working, but I can't remember if that was only with the key on and the engine off or what. Sorry if I'm spreading misinformation.