I believe the answer is with using PKG_CONFIG_PATH, as defined here, and in the answer given here.
I also found this on the github page of the directx-headers...
Pkg-config: Use Meson to build this project, and the resulting
installed package can be found via pkg-config.
Found this answer, also useful.
Finally, I found this, which was useful, and provided the information I wanted to know regarding Cygwin searching the PATH.
Significantly Edited [SOLVED] -
The solution : Guide to pkg-config
On a typical Unix system, it will search in the directories
/usr/lib/pkgconfig and /usr/share/pkgconfig. This will usually cover
system installed modules. However, some local modules may be installed
in a different prefix such as /usr/local. In that case, it's necessary
to prepend the search path so that pkg-config can locate the .pc
files.
$ pkg-config --modversion hello
Package hello was not found in the pkg-config search path. Perhaps
you should add the directory containing `hello.pc' to the
PKG_CONFIG_PATH environment variable No package 'hello' found
$ export PKG_CONFIG_PATH=/usr/local/lib/pkgconfig
$ pkg-config --modversion hello
1.0.0
What was required is using export VAR=value(or path-to-directory)
After this, the path will be found successfully.
So to find Third-Party libraries etc., simply use the export variable command.