I took the Neck Ringer down to the lab today to test the output. I ran a 100mV pp sinusoid through a 47k resistor into the input jack with a few different known guitar frequencies.
It's working perfectly as an octave-up / frequency doubler, as shown in the oscilloscope output below:
The longer wave is the input fed from the frequency generator and the shorter wave is the output of the Neck Ringer. You can see the output will go through 2 cycles for every 1 at the input, doubling the frequency. The input wave was set to ~330hz (E4, open E) and it output a wave of ~660hz (E5, 12th fret). I noticed it also changes the shape of the wave, I don't think it's a true ring mod but you can see the wave "pinched" halfway through each cycle.
I just need to cut the board to size and get some plastic standoffs and we'll call this one done.