The cigarette lighter and clock light in a 2003 Pontiac Grand Am are not connected to the same fuse. The cigarette lighter is powered by the fuse labeled "CIG" in the fuse box located under the instrument panel, while the clock light is powered by the fuse labeled "ILLUM" in the same fuse box. If either of these fuses blows, the corresponding component will not work.
To check the fuses, turn off the ignition and open the fuse box. Use a flashlight if necessary to locate the fuses labeled "CIG" and "ILLUM." If either of these fuses is blown, replace it with a new fuse of the same amperage.