32d Armored ("armoured" is the British spelling, which often creates confusion) was an organic element of 3d Armored Division (the division's nickname was - and is -"Spearhead"). Constituted as 2d Armored in January 1941, the regiment was organized at Camp Beauregard, Louisiana three months later and redesignated 32d Armored the following month. Regiment landed in France 23 June 1944 and was inactivated in Germany 10 November 1945. Five campaign participation credits: Normandy, Northern France, Rhineland, Ardennes-Alsace and Central Europe (campaign credits to which Shackleton would be entitled would depend on when he joined the regiment - this can only be determined by examining unit records).
The 32d was one of four armored regiments that remained intact during the war (all others were reorganized in 1943 to form individual tank battalions). Company C, was an element of the regiment's 1st Battalion. AIR/GND LN - Air-Ground Liaison - co-ordinated operations of aircraft providing close air support with operations and movements of ground units to which air support was being provided.
Except for service and support units which, for the most part, served in their normal roles, all units involved in the occupation were essentially military police; many being formally redesignated constabulary squadrons and regiments. With no more than the info provided, it's impossible to determine which unit he served with during the occupation.