I don’t own one, but I’ve seen the insides of a couple (there are at least three or four that I’ve seen here in Australia). The metal box houses a pre-amp and 9v battery. The Mugen 21-labelled white plastic box houses slider pots which handle volume and tone controls. You can see how the red and black cables hook the controls back into the pre-amp. As far as I’m aware, most of the art is in the type and placement of the mic.
The pre-amp always seemed a little vanilla to me - the tone controls are voiced so that you can EQ at shamisen frequencies, but they just seemed like a passive two or three pole tone stack with no special sauce in terms of filtering or modulating the signal coming off the mic.
The black wire going off to the side of the dou is just grounding for the jack, I think. You can see a length of bus bar against the wood, and it doesn’t run back into the pre-amp. If it were doing anything clever like a quasi reverb spring, you would need to see a reverb driver and a connection back to the pre.
Because I don’t have a Mugen, my approach to running a pickup is a bit different. I use one of these:
http://www.b-band.com/index.php?mact=Products,cntnt01,details,0&cntnt01hierarchyid=2&cntnt01productid=1&cntnt01returnid=151
It’s a transducer in a thin ribbon style which I picked up for cheap on Evilbay. I place it on the front skin of my shamisen and put the koma on top of it, and tuck the jack/pre-amp in near the neo. It’s not exactly like the Mugen sound, but it’s pretty good and none of the Mugen owners has complained about it. The output is enough to drive whatever pedal and amp I’ve thrown at it (currently playing through anything from a Roland Cube 20 to a 30 watt Laney 2x10 valve combo).
In my experience, shamisen and distortion are a tricky mix to get right. The overtones (and the short note decay) peculiar to a shamisen give you some difficult things to work with, and the general lack of lower frequencies can really rob you of some of the material to drive a distortion so it can end up sounding pretty thin and fizzy. Happy to share what I’ve experimented with, it can just get a bit tedious for those who aren’t totally into discussions of the Most Awesomest Distortion Evah.