It wasn't German air force base but contingent of German air force were at NM USAF air base for training like from time to time so many foreigners training at Pensacola and other military installations in U.S. mainland, it wasn't German air force command and control like NATO at the biggest U.S. Naval base.
Ok, "Tactical Training Center". With a permament contingent to serve the pilots that cycled through. The German Air Defense Training Center was located nearby.