It took a whole 16 years between Congress authorizing a proclamation and President Johnson making it official that a day shall be set aside for the remembrance of lost veterans. Even though Europe had been in peace, much had happened between that time: shattered economies rebuilt and rearmed against the Soviet threat, and as Johnson himself proclaimed in his speech, a new generation of young warrior was bleeding and dying in Vietnam. Occupation forces morphed into reconstruction and mutual defense forces in Europe and Japan and sat in for the long haul - this was their new home. As such, they needed cars. A whole new automotive subculture was born, and would be imported back to the 'States with many (but not all) of these brands occupying lofty niche or even mainstream corners.
Europe Proves Smaller is Better
When my dad was stationed in Munich deep in the throes of the Cold War, he bought a little used red Neue Klasse 2002 from a fellow GI whose ticket was up and needed to go back home. This made him the third owner; his buddy bought it from a local who needed it excised from his garage due to a few rust issues. Neither he nor my dad understood why - the little notchback coupe held up well despite the cosmetic blemishes and lived up to the vaunted reputation of "Ultimate Driving Machine" BMW coined up decades later. So much so that GI #1 wanted to have it DOT legalized and bring it back with him, but the rust combined with the high cost of making that happen killed that idea (along with the fact that they had started selling the Neue Klasse in the 'States too). Even my dad thought about it but, alas, it was sold off to be some Fraulien's first car.
image from David Greenlees and The Old Motor
In the late 40s GIs (or rather, actual officers) started bringing "Gentlemen's Cars" home with them. They saw a bunch of British blokes looking quite spectacularly British in their British roadsters, and thought, "hey wait a minute I can do the same thing in my home!" The MGs and (for the better-heeled officer) Jaaaaaguars exposed the American public to cars that coughed power from their sub-100 HP engines (or just over 150, in the Jag's case), but were so light they didn't need the flathead V8s that came in every basic Ford economy car. Not to say that the flathead was a fountain of power either. In fact, 160 HP out of the Jag's 3.0 liter put them in the exact class as Ferrari - when you read up on the history of the Corvette and you see a citation of something about the European roadsters domineering and inspiring the 'Vette, they really mean the XK120 specifically.
image credit Alex Norstrum via Wikipedia
Not everything was direct from Britain or Germany. The very first truly new car my dad ever bought could hardly be any newer - a Volvo 242 bought straight off the assembly line while at the factory in Sweden, and that he indeed took home with him. I learned to drive stick on that thing, which after 20 years or so was like trying to change gears on the Queen Mary II. European makes of all sorts and all countries got exposure, and convinced them that they had a fighting chance in the North American market. Not all of them made it as the infamous Lucas quality control in particular chased out the British brands, but the Germans and to the lesser extent the British are here to stay with the Swedes still hanging on.
image from the Daily Mail poseur attire sold separately
The iconic officer imagery was hardly limited to four wheels. Thousands of GIs returned with new skills sets provided freely by the government, including piloting aircraft and motorcycles. At home, they formed hundreds of motorcycle clubs, including direct descendants of segregated military units. The men that went back naturally gravitated towards the most iconic of American steel, Harleys and Indians. Those who stayed overseas experienced the spunky thrills of small parallel twin or even single-cylinder bikes with badges reading "BSA," "Norton," "Triumph" and "BMW." The 60s Mod Culture and the phenomenon of the Cafe Racer cemented the little sports bike into its own standing.
Across the Pacific
The rise of Communist China and the Vietnam War meant hundreds of thousands of GIs stationed or at least passing through Japan, building on the legacy of the postwar occupation forces. Unlike the troops stationed on the Isles or on the Continent, it took a while for American GIs to really find something that would catch their attention in the Pacific. What had arrived in the initial rebuilding stage was simply too small and too anemic for American tastes. Plus, with urban roads still in ruins and a lack of road networks connecting major population centers, Americans preferred to roll around in their Jeeps (and later, the Japanese Jeep "knock-offs" built to satisfy local demand as the "genuine articles" were sent to Korea).
The American occupation ejected much of the top leadership at Nissan, citing their use of forced labor in their Manchurian production plants. Yutaka Katayama - who was appointed the head of these very same plants in 1939 but found labor conditions so appalling that he demanded to be sent back to Tokyo - was put in to take charge of all Nissan operations. His Manchurian experience convinced him to apply the name Datsun for American-bound exports. He also wasn't very happy with the fact that Americans in Europe were more than willing to bring back Mercedes and Volkswagons but few were clamoring for his products. The Datsun 1600 and later, the 240z were the first successful attempts to appeal directly to the American market.
But remember that thing about Japanese "Jeep Knock-Offs" being very useful for getting around Japan right after WWII? Oh yeah, people noticed, and it's perhaps Japan's greatest automotive legacy next to the blandmobiles from Toyota. The legend of the Hilux is as enduring as the truck itself, even becoming a key weapon against heavy, sophisticated Soviet armor in the aptly named "Toyota War." We remember the Volkswagons on our own roads, but for GIs fighting overseas today the Hilux has become ubiquitous and iconic on its own.