85th Armored Reconnaissance Battalion was constituted and organized at Fort Knox, Kentucky in 1941, the reconnaissance element of the 5th Armored Division. Later redesignated 85th Cavalry Reconnaissance Squadron (Mechanized), remaining assigned to 5th Armored Division. Your Dad joined Company D in 1942 and was later transferred to Troop F (in cavalry units, a company is designated or referred to as a "troop").
Your Dad apparently joined the squadron in early 1942 upon returning to the Zone of the Interior from Panama. Armored units trained extensively in every possible climate prior to being sent overseas (Camp Cook, for example, was a desert warfare training center). This is the reason for the various addresses.
The fact that he was a Staff Sergeant in February 1942 and a private a year later indicates only that he was reduced in grade -this doesn't necessarily mean he was "busted" (reduced in grade as a result of disciplinary action). Throughout the war, individuals refused promotions and/or took voluntarily reductions in rank or grade for a number of personal reasons.
The 85th was an element of 5th Armored Division throughout the war. You can contact the division's veterans association at:
5th Armored Division Association Will Cook, Secretary 13344 Luthman Road Minster, Ohio 45865-9375 (419)628-4032 < wc5adWW2@wesnet.com >
Perhaps they can put you in touch with somone who remembers him.