From what you said I’m unsure of whether the fan disconnect changed or did not change the nature or strength of the noise. Basically though, you are testing for two things…cross-talk and power source noise (it is possible that both occur in some mix). Distinguish between strength of noise and other qualities, like frequency or spectrum of noise (strength versus quality).
Removing a noisy power consumer (e.g., an inductive motor load) should reduce strength of noisy power delivery since this is essentially a load modulating power rails and the load is removed. Cross-talk would tend to remain after removing the fan load if the power rail modulation is not the issue since non-power circuits would be responsible.
Ethernet cable does not significantly change power rail load, so changes in Ethernet cable changing noise character would tend to lean towards cross-talk. Fan disconnect leading to change in nature of the noise without any reduction of noise would also tend to lean towards cross-talk. In the case of power noise you can adjust components, typically capacitor values or type of capacitor. In the case of cross-talk, typically it would mean re-arranging trace shapes and locations (in wires that means twisted pairs and shielding changes).
The microphone wire itself can be (and usually is) a very significant contributor towards cross-talk (in this case cross-talk with environment outside of Jetson). I think the connector is capable of detecting if a microphone is plugged in or not, so continuing to record without a microphone as if the microphone were present may not be easy. The goal of testing with no microphone but with everything else active and recording is to see how much of the noise is from JTK1 circuitry and how much is from the microphone. What you would have to do is to wire a small plug with the same connector as the microphone and put a pure resistance across as a fake microphone load…the shorter the cable the better. With that you could tell if the noise still exists without the microphone.
I do not know what impedance the JTK1 wants for a microphone, but noise from cross-talk of the microphone itself may go up if the actual microphone impedance differs too far from what the design calls for.