How to trace a wire hidden behind plywood wall?
Do this with POWER TURNED OFF.
Use a 74HC14 Schmitt Trigger IC, in a self_oscillating R+C feedback.
The edge speed will be plenty fast to produce numerous responses in an AM radio, if you have a 50,000 Hertz oscillation frequency. Approximately, not crucial.
And the 5 volts operation also helps.
Pick one of the 6 available Inverters.
For that inverter, connect 1Kohm, or 1.2Kohm, or 1.5Kohm, or 1.8Kohm or 2.2Kohm from output to input.
Select a small capacitor to use on the inverter_input pin.
For 50,000 Hertz (20 microsecond period), you need about 10 microseconds time constant. Since varying the VDD will change the frequency, you need not be precise. A cap of 0.01uF from Inverter input_pin to Ground will, with 1Kohm, produce ( R times C ) 0.01uF * 1Kohm = 1e-8 * 1e+3 = 1e-5 = 10 uSec TAU.
To provide VDD (approximately +5v), use a 6 volt battery with 1N4001 or 1N4148 in series.
Have 0.1 or 0.01 uF cap across the VDD and GND pins: pin 14 and pin 7.
Have a small cap from inverter output to a wire with alligator clip, that attaches to the wire.
Notice there is NO RETURN path.
And you must have POWER TURNED OFF.