91 caprice brake lights, intermitant running lights

the fuse to the running lights will blow from time to time. i know i can put a fuse back in, and they will work only when the clock on my radio dims when i turn on the headlights. 
 Just like i know the fuse blows when the headlights are on and the clock is dimmed and then comes on full. i am checking bulbs, but I haven't found anything unusual and all bulbs light when problem is not occurring.