One of the lights stays dark. Best to quickly replace the bulb. It stays dark, so it’s not the lamp. There are a lot of other sources of faults. Here are some examples.
Sometimes, especially in rear lights, it’s enough to jiggle the lamp or quickly remove it and put it back in. If the light then comes back on, the problem isn’t so much a loose contact but rather corrosion. Verdigris on copper contacts and similar oxidations have an insulating effect. The thin layer can often be removed with just a paper tissue. Tougher cases call for a file – if need be a nail file – or sandpaper.
Broken cables are tougher to deal with. They mainly occur in places where there’s a lot of movement such as the links to rear doors or trunk lids. If for example both license plate lamps suddenly give up the ghost, a lot points to this annoying fault. Repairing broken cables is complex and is a job for professionals.
Blown fuses are easier to deal with. Sometimes to blame are halogen lamps from headlights which burn out themselves, drawing a high amount of current in the last second of their lives. You can tell by the lamps briefly flashing before they go dark once and for all. Fuses are generally easy to change. The difficult part is to find the blown one because in many cars they are installed in several places. The manual will help you locate it. Well, and then you’ll also need spare fuses of course. Sometimes car manufacturers provide some in the fuse box’s unused slots. Otherwise the replacement lamp boxes from Osram contain the most common fuses.
Sources of faults in switches and relays are really complicated and need to be sorted out by a mechanic. Unless someone simply forgets to put the light switch from Off back to Automatic after replacing the lamp. Wouldn’t be the first time.