I did some calcs and measurements white aligning the FM detector in the 1963 Panasonic RE tube FM receiver.
The signal generator which has FM modulator was connected to 10.7 MHz IF upsteam of the last IF amp, to align the detector.
This detector has 3 resonant frequencies, it would be necessary to destroy the coils to see the connections, so I assume the quadrature coil has 2 coils each with a different inductance or else one coil is wound in opposition ( centre tap soldering under the wax.)
The operation can be viewed by connecting 'scope probes to each of the 2 diodes, and observing the amplitude changes while manually stepping the deviation.
The positive diode is connected to the coil with highest resonant frequncy.
So as the deviation goes positive the voltage rises on the upper resonance , the upper diode conducts, pulling the output high.
As the deviation goes negative, the voltage rises on the lower resonance and the lower diode conducts , pulling the output low.
I think that both diodes are conducting with zero deviation, however I could not measure that with the limited test points added.
I also put some calc amd measurement to support my post #4, that the published descriptions of operation by phase change on the quadrature coil are not valid.
FM broadcast has the highest modulation index compared to other communication.
Even with high deviation of 75 kHz, it is not possible to get anywhere near usable phase shift at 10.7 MHz, confirmed by today's Q calculation and measurement on page 2 below, showing phase shift of only 4 degrees at full deviation..
https://app.box.com/s/v5kvqi88jc2zkkn2w52i8qfd2veyuvrw https://app.box.com/s/avi9llwy9ykosw4hvjiwiln3v8sqprv4