Where is the backup light switch on a 2001 Buick century?

The backup light switch on a 2001 Buick Century is located on the transmission. It's not a separate switch you'll find on the dash or under the hood. It's a mechanical switch activated by the transmission's shift linkage when you put the car in reverse. Therefore, you won't find a "switch" in the typical sense to replace; the whole assembly is usually replaced if faulty.