Can't get the reason for a dead silent effect, but let it be..

For MAX pot set fully CCW, IC1_A turns into unity gain buffer (signal on pin 7 is in phase with pin 5 and of equal amplitude)..
(meaning whatever comes into pin 5 comes out of pin 7 identical..)
250k pot, C11, R11, R10 and C10 form a rather complex LPF with 250k pot serving as the "upper" element..
Any non-zero resistance between pot wiper and lug 1 is added on filter's "lower" part, hence raising its corner frequency..
(which frequency is drastically lowered again by making C11 bigger..)
IMHO, hot humbuckers might upset VR, dominating op-amp's power supply rejection, hence passing AC into pin 5..
(interpreted as a faint input signal..)