I was able to silence the tuning "tick" by inserting a 22 ohm, 2 watt resistor in series with the Raduino power wire and connnecting a 470 uF capacitor from each end of the resistor to ground (One resistor, two capacitors.). ?You can easily do this right on the back of the volume control/power switch. ?This indicates that it is a power filtering issue. Lower values of resistor and capacitors will work but I have not determined the optimum values. ?Some serious bypass treatment on both input and output of the Raduino's 7805 regulator should help.
Another suggestion to reduce audio distortion is to connect a 10 uF capacitor between pins 4 (gnd) and 7 (internal bypass) of the LM386.
K9AC