HONZA: i'm not sure when the US started building factories in Taiwan or having Japan make stuff for us, but it wasn't long after WWII. if you have more information on that let us know.
Anybody know when the US started importing from Japan. or Taiwan? not certain this is where these vises were made, but since they have parts of several other vises unless Sears owned all the patents my thinking is the patents wouldn't have been worldwide back then so all these cool ideas could have been put into one vise.
According to my experience with other collectibles:
After the war, Japan was forbidden to export anything for two years. From 1947 to 1952, all exports BY LAW were required to bear the marks "Occupied Japan" or "Made in Occupied Japan." If an item could not be marked that way because of the material, it had to have a stamp or a sticker. In instances like mid-fifties Christmas lighting, the mark dcould be on the packaging. Even 1952 and after, they were still required to be marked Japan in some fashion. Exports of the 1950s to early 1960s comprised mostly five-and-dime items, some ceramics and even fishing tackle. One of the tools that were exported in the early 1950s was the Allenite brand--I have one of these early Allenite 1/2" drive pear-head ratchets, made as a knockoff to Proto/Penen. The selector cam is stamped metal and had to be re-adjusted and the original bolts were rotted and I replaced them with stainless (weird, but the threaded holes were SAE not metric!), but once refurbished is a killer ratchet with almost no backdrag. Hey...you figure they knew how to make formidable battleships and Zeros, so they had to have some idea how to build quality. Even so, the wrench is clearly marked Japan. If any vise was imported from them during that time, it would have had Japan marked in it.
As far as Sears, I know they started importing Japan tools (with the BF code) starting around 1962 when Japan began to concentrate on higher end products like electronics and moved away from the dime-store stuff, leaving that market more and more to Hong Kong and Taiwan (the early Taiwan imports are marked "Republic of China, Taiwan). I personally don't know of any Sears hand tools made in Japan prior to the early 60s.