After doing a bit more research, I now believe Konstanz is an unlikely location for this unit. Konstanz was captured by the French Army in the latter days of WWII and remained in the French occupation zone after the war. If this unit had about 150 men (based on observed weapon numbers), the "survival rate" of its Lugers is about 7% which is rather high and much higher than would be expected from an area controlled by the French. I think a location in Bavaria which was captured and occupied by Americans is much more likely. Kempten would be a candidate but that's highly speculative.
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