This is from a Super-Takumar 135/3.5 and is probably similar to your lens. The typical Tak construction is a one-piece mount assembly like this. It's attached to the rest of the lens with screws under the aperture ring. You have to take the front of the lens apart and focus ring off before you can slide the aperture ring off, catch the ball bearing trapped under it, and see these screws.
The M-A switch has a tab that goes through a slot in the casing. It attaches to the darker brass ring with the two slotted screws on the right. (Follow that ring around to the other side and see the flat spring that clicks between switch positions.) You can see a light shield here that is probably helping block a light leak on your lens.
A quick fix is to bend the tip of a paperclip to a 90 degree angle, stick it the slot for the M-A switch and into one of those screw holes. Then move the internal brass ring to the M position. The aperture ring now controls the aperture directly. Tape up the slot and use the lens.
The 200mm lenses might come apart easier from the front, but I've never had one of these apart. On the 135/3.5, you have to take off the trim ring, remove three screws holding the filter ring, remove three screws holding on the focus ring, then slide off the aperture ring. Because the 200mm is longer, there is often a way to remove the front part of the lens in one assembly. I know for later lenses, you can focus to the minimum distance, grab the front barrel and unscrew the front part of the lens. Then figure out how to get the focus ring off.