Wired to the same system as your headlights, the tail light assemblies illuminate whenever you turn the light switch. A relay allows power to reach the tail lights. If it fails, then there won't be rear lighting. A blown fuse can have the same effect. One of the most common reasons for failure, however, is when you need, for example, 2003 Buick Century tail light bulb replacement. There are longer lasting bulbs such as LEDs, but many people still use halogen bulbs. These are inexpensive to replace and can quickly resolve the problem. On the other hand, issues such as worn sockets, connectors, wires, and harnesses require you to replace the assembly. Corrosion can be problematic as well, especially when moisture gets inside through a cracked cover or lens. Broken lenses and interior fogging can affect light output and may warrant getting a new 1996 Buick Century tail light assembly.
The rear of the tail light assembly can be reached through the trunk. Your car's repair manual will show how to remove and service it. A bulb can be unscrewed through the part's back, and you can replace a 2003 Buick Century tail light assembly by removing the screws or mountings and prying it out of its frame.