J. Falk'S company (who had had business ties with Schoenner and Carette much earlier) merged with the remains of Bing Werke in 1932 (so Bing was split up and the steam engines part was swallowed by Bing, not vice versa, as I always thought). As Falk was a "non-Arian" company in the crazy ideology of the Nazis, Falk was wise enough to sell the company in 1935, the toy production ceased then - nobody knows exactly what happened to J. Falk (some claim he could escape ani terror in time; all this information from Kaiser/Baecker's famous book on German steam engines).
So you have not only bought a nice steam engine, but an interesting witness of German history as well.
Bing-Wolf (the badge looked different from the famous "BW"-badge for Bing Werke) was based in New York, formed in 1928, if I am not mistaken, and was a kind of joined venture of Bing, Nuremberg and an American importer. Once in a while you find Bing engines, often electrically heated, with their badge (which can be traced via the internet) offered in the USA today.
The base of your engine (smoked / flamed) looks very much like the bases used for engines made by different German makers (Doll, Bing etc.) for VEDES (= Vereinigung Deutscher Spielwarenhändler / Organization of German Toy Retailers). But in that case, it should also wear the VEDES-badge. One can only speculate if JF/BW simply coxed the design or used some bases they still had in their depots.
Hope you don't have to wait too long for it!