I seriously doubt it and don't think it's recommendable...
All I can say for sure is that the TK20's tube is very different from the TK11 (which should be pretty similar to the Tk12) -different threads and different diameter- and that is mainly because the Tk20 uses AA's and is not recommended for other types of batteries.
I think it's unlikely to fit but the thought occurred to me. The TK11 tube is not like the TK12, and the TK20 has a very thick body. TK20 tailcap and head thread diameters are 22.4 and 23.9mm respectively. Also the TK20 happily accepts 2 L91's with a combined voltage of 3.6v.
As Cataract mentioned, TK12 body has the new trapezoid thread so I doubt it'll fit on Tk20 head, but interesting idea, let us know how it goes :naughty: