2003 Pontiac Bonneville dome/trunk light not working; back

Dome and trunk light are not working. Fuse has been replaced 2 times. After replacing the fuse it works for only for a short period of time.
Now I am also having problems with the tailamp and tail/brake lamps staying on when I turn off the engine. This seems to be an intermittent problem. When these lights stay on after the engine is truned off it drains the battery.
I am assuming these problems are related.