String Harmonics

Hey everyone! I just got a new (used) dulcimer which is going to be my main DAA noter & drone instrument. While playing it, I kept hearing high-pitched ringing every time I lowered the noter onto the melody string. This happens even if dropped from a very low height. I can only avoid it by sliding the noter all the time. 

Is the string too tight? Too low/high action (don't suggest checking with dimes and nickels—I haven't had any of them in 20 years)? Wrong gauge (I have .12 gauge with 26.5 VSL)?

Any suggestions are highly appreciated. :)