Tricone

I have an old (1930s) National square neck Tricone that has developed an intermittent buzz-like rattle. If I keep my right hand close to the bridge it doesn't seem to occur. If I move away from the bridge, I hear it, especially when playing with my index or middle finger. My guess is that when I strike a string with my index or middle finger I am lifting the sting slightly, which somehow mysteriously contributes to the cause of the buzz. It is rare that I get the buzz when striking downward with my thumb. I have replaced the strings, but still the buzz persists. Any suggestion that would help eliminate the buzz (or even help diagnosis the cause of the buzz) would be much appreciated.

Jim McCarthy