I've owned two Kowa's, a SET and a SER T. If my memory serves me right the shutter is in the body in front of the mirror. The way it worked, if I am correct, is there is also a light curtain behind the mirror.
When you look through the camera normally the mirror is down, the light curtain behind it is down, and the leaf shutter in the body is open. When you press the shutter release to take a photo the leaf shutter closes, followed by the mirror raising, then the light curtain opens, then the shutter re-opens and exposes the film and closes again. After the film is exposed the light curtain closes, followed by the mirror dropping, then the shutter re-opens. Of course while this is going on the aperture blades must also work, too. Needless to say, there are a lot of moving parts in there. Both my cameras suffered the same failure, shutter problems. Until they did, both provided very good service. However, when they did no one would work on them. I assume yours works in the same way.
Edit, found this on the operation. http://taunusreiter.de/Cameras/Kowa_SETR_eng.html
Leaf shuttered 35mm SLRs are notorious for this sort of thing and VERY difficult to have repaired. Their medium format cousins are much more blessed in this regard.