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dir/pydir/Tools/buildbot/external.bat downloads tcl/tk 8.y.z into dir/tcl-8.y.z and dir/tk-8.y.x and compiles them into dir/tcltk. Of critical importance are dir/tcltk/bin/tcl8yg.dll and dir/tcltk/bin/tk8yg.dll (where y is currently 5 or 6.
dir/pydir/pcbuild/_tkinter.vcxprog compiles _tkinter is such a way that it looks for the two dlls 'everywhere' (in pcbuild itself and 5-10 other, non-existent directories) other than where they are.
The current manual fix, reported a year ago on core-mentorship list, is to copy the two .dlls into pcbuild. This should be done by external.bat.
A possible alternate fix would be to revise _tkinter.vcxproj so that _tkinter looks for the .dlls where they are. However, since multiple tcl/tk versions are compiled into /tcltk, this would break installations that use one 'dir' for multiple 'pydir's, as shown in the devguide. Currently, the .dlls must be copied into pcbuild before they get overwritten by another version.

> compiles _tkinter is such a way that it looks for the two dlls 'everywhere' (in pcbuild itself and 5-10 other, non-existent directories)
I think you're confusing the finding of the tcl/tk DLLs with the finding of init.tcl; the DLLs are searched for on PATH (as I understand it, just like any other DLL), while init.tcl is searched for in several places hard coded deep in bowels of Tcl (see #20035).
Python 3.5 (default branch) builds Tcl/Tk as part of the build solution rather than as part of external*.bat, and copies the DLLs to the output directory as part of the new system. 3.4 and 2.7 could be fixed to copy the DLLs as part of external*.bat, but will have issues similar to #21059 without some kind of fix like #20035 (which is currently only targetting default branch).

I am quite aware that the two searches are different. tcl8xyz.dll and tkxyz.dll must be copied from ../tcltk/bin to pcbuild while init.tcl must be left in ../tcltk/lib/tcl8.x, where x is, now, '5' or '6'. Since compiling tcl/tk clears tcltk/, it is impossible to simultaneously run 2.7 which requires tcltk/lib/tcl8.5/init.tcl and 3.4/5 which require tcltk/lib/tcl8.6/init.tcl.

Since the two .dlls must now be copied manually (still undocumented?) for tkinter to work, I fail to see the problem with having the copying done automatically in external.bat right after the compile that creates them.

I believe this has been fixed some time in the last few years; Terry, please reopen this if I've missed something.

The fixes, attached to other issues, works flawlessly for me.