I got into a Z620 here, and it is unclear to me too. There are the two blue USB3 ports available at the front face of the worksation, and the one black top USB2 just above them, so you have accounted for those. The 4 wires you mention go out from that header's bottom row of pins via a small diameter insulated wire bundle, but then enters that black box you show. You'd need to get inside of that box to figure out where they come out, but that will probably break it.
A few ideas.... in the service manual about header #27 HP talks about the front power button, LED, and speaker. But not Mic. But those 3 wires usually would come back to the motherboard via the front cable to header #27 (from past workstation engineering) and maybe they just left that off the "Mic" notation. There also are rarely used options such as the side cover alarm device that alerts if the side door had been opened, etc. Look into those options.
Honestly, your best bet would be to get ahold of Dan, and if you had a bare Z620 motherboard there might be some hints in tiny printing on the PCB at that far lower edge just beneath the header.
Let us know..... very creative solution to getting front USB3 ports into a Z600. Another way would be a 5 1/4" to 3.5" adapter for one of your optical drive bays, and put in the Akasa 3.5" adapter that comes with a nice long cable going back to feed off the standard motherboard/card USB3 header. That cable is more than long enough... they PhotoShopped it for this pic. The quality is A+, the device is designed to mount a 2.5" drive if you want (I did not) and that is exaclty what I used in my USB3-in-xw6600 project:
