My husband was stationed 3 different times in Germany. The first time from December 1961 to September 1966. The second time from September 1968 to December 1970 and the third time from August 1977 to May 31, 1979, I became a naturalized US Citizen on June 12, 1977 in Junction City KS.
Yes, I had to register my son also after his birth at Landstuhl. He was issued a German birth certificate at birth.
A child born abroad to one U.S. citizen parent and one alien parent acquires U.S. citizenship at birth under Section 301(g) of the INA provided the U.S. citizen parent was physically present in the United States or one of its outlying possessions for the time period required by the law applicable at the time of the child's birth. (For birth on or after November 14, 1986, a period of five years physical presence, two after the age of fourteen, is required. For birth between December 24, 1952 and November 13, 1986, a period of ten years, five after the age of fourteen, is required for physical presence in the United States or one of its outlying possessions to transmit U.S. citizenship to the child.) The U.S. citizen parent must be the genetic or the gestational parent and the legal parent of the child under local law at the time and place of the child’s birth to transmit U.S. citizenship.