Wow, I admire your determination to snoop this out! While I don't have the answer, I do want to help...
By swapping out mics and even the cable, it sounds like you've isolated the problem to the head unit. I'm not sure if the mic signal is used and processed in the head unit or in the hide-away unit, but the next step might be to test continuity on all wires between the two, check for loose pins, etc.
Assuming that's all sound, I'd just assume it's a bad unit.
If you REALLY want to go nuts, maybe you could spend a minute or two trying to figure out how the N2 detects if you have a mic plugged in or not. As it's a standard jack, I assume a ground is toggled (either broken or shorted) when you plug the mic into the cable. I'd get out my multi-meter in continuity test mode, contact the leads to two of the three pins on the connector and see what pins short or break when you plug the mic into the cable. For example, maybe L and R are shorted until you plug in the mic. I don't know specifically for the N2, that's why you'd need to test. Once you know how it detects the mic, I'd bypass the connector altogether and just short the pins (or maybe take a pin out, if that's what you find) on the connector and plug it all in. If it shows that the mic is plugged in, then you know it's the cable or the mic.
