Berlin Brigade, August 1972 to January 1975. Started out in 4/18 then we were redesignated in place to 4th Bn 16th Infantry to match the other two infantry battalions there, 2/16 and 3/16. However, this is the first I've heard of that German marksmanship badge.

Fwiw, Berlin was still officially an occupied city, we had the same unit patch that Eisenhower wore in WWII with the addition of the word "Berlin".

[Linked Image from sparks-military.com]

Gunnery, gunnery, gunnery.
Hit the target, all else is twaddle!