Hi Oleg,
The symptom of less output, no hum-cancelling null, and especially the microphonic sound when tapping the dual FET all indicate that the pickup coil is not connecting to the preamp. This could be a failure in the tiny magnet wire inside the pickup, or in the connector.
Your ohmmeter measurement is the right thing to do, and the values you found for the bass pickup and hum canceller are what is expected. As you noted, there is a resistor in parallel with the pickup, but that is only there to provide bias to the FET gate if the pickup is disconnected, and the value of the resistor is 22 MOhm so with the pickup in connected the resistor value is so high that it doesn't affect the approx 3 KOhm value of the pickup coils.
The microphonic noise when tapping the FET is actually good and that indicates that the preamp is functioning properly (with the extremely high 22 M resistor, microphonic noises are easy to produce). And if the pickup coil were open, then I would expect more noise when you tap the cable than you produced in the video...the coax has teflon insulation, and this material easily generates triboelectric signals so is microphonic when connected to a high impedance. The microphonic noise is completely shorted out by the source impedance of the pickup, so when all things are working properly, the cables are not very microphonic. Likewise tapping the other FETs didn't produce the microphonic noise, as the noise is effectively shorted out by the pickups.
The gold connectors are originally designed for microwave gear (like Radar sets) and have precision tolerance limits to perform in that application. They are installed on the cables at the factory with specialized tooling as field tools would not achieve the required precision for use at microwave frequencies.
As being coax connectors, with one center conductor, and the larger outside (shield) connection, it is normal for you to be able to rotate the connector as you discovered. So we don't have the parts siezed and joined permanently.
What is unexpected is the low reading of 1.3 kOhm and the intermittent high reading. If the connection were intermittent, you would expect the high reading, but when held just right the lower reading would be similar to the other pickups, not the lower reading you measured.
There is one possibility, which is the where the center conductor of the coax cable solders to the circuit board. That center conductor is very small and delicate, and you can see the white tiewrap (Panduit) nylon devices used as strain relief at the edge of the board on each of the coax connectors. I'd like for you to examine the center conductor on the top of the board
with a magnifying glass or microscope and make sure that the wire hasn't broken or moved and is shorting to something else on the board. The center conductor is very fine, and even then it's stranded, so the individual stands are extremely fine.
If the center conductor looks good when magnified, then I'd like to you to pull harder to separate the connector. As you can see on the Bass pickup connector that you were able to separate, on the connector half that is still connected to the printed circuit board, there is a tiny groove in the outer conductor where it mates with the pickup end. And if you look, again with a magnifying glass and bright light, you will be able to see on the pickup side of the connector that there are six slots that were sawn to make arc tabs. At the end of each tab the metal is formed to make little protrusions that drop into the groove on the pc card end to provide the retaining function. As others have said, these tabs are delicate in the unmated condition.
Also rotate the two halves of the connector when you are pulling apart with a combination pulling and twisting motion to assist the locking protrusions to climb out of the groove. You can pull hard to convince the connector to disconnect. Note likely that you would break the connector, but at this point since that channel is not working, we don't have anything to loose. Then you can remate the connector and see if that restores operation. To reconnect you have the halves lined up, and then carefully push together, and often assisted with a twisting motion while you push to help the protrusions climb up to let the connector mate.
Then assuming that things come apart, get remated and the problem is still there, as Jimmy started to write, you would reverse the two pickups, and connect the bass pickup to the Red printed circuit connector, an the treble pickup to the Blue PCB connector and see if the problem has moved to the other channel (and you can also verify with the Ohmmeter to measure the pickup resistance.
If the connector breaks, or we determine that the issue is in the connector, then Mica will send you a new connector. Is your address the same as before? I'm hoping that things will clear up with remating the original connectors, as it is a difficult job to strip an prepare the end of the cable for soldering to the printed circuit card, as the teflon insulation is tough and it's easy to nick or break the extremely fine strands of the center conductor, but with care, I'm sure you can do it if necessary. If the pickup side of the connector has to be replaces, then you have to splice it in on the existing wire, and that involves stripping and preparing both sides in order to solder the new connector to the existing pickup lead. Fortunately, the teflon is totally heat resistant to soldering temperatures, so you don't have the problem of melting the plastic insulation when soldering.
-ron
