GNU texinfo directory search method?

Yes, info does have a default value for INFOPATH compiled-in that it uses if you don't have INFOPATH set in your environment. (Also, if your INFOPATH ends with a colon, then the default path is appended to your value.)

The default DEFAULT_INFOPATH is .:/usr/local/info:/usr/info:/usr/local/lib/info:/usr/lib/info:/usr/local/gnu/info:/usr/local/gnu/lib/info:/usr/gnu/info:/usr/gnu/lib/info:/opt/gnu/info:/usr/share/info:/usr/share/lib/info:/usr/local/share/info:/usr/local/share/lib/info:/usr/gnu/lib/emacs/info:/usr/local/gnu/lib/emacs/info:/usr/local/lib/emacs/info:/usr/local/emacs/info (but it can be changed by defining DEFAULT_INFOPATH while compiling info).

There's also a INFODIR variable that can be set while compiling info. If set, it gets included in the path after the INFOPATH environment variable but before the DEFAULT_INFOPATH.

I don't know any way of asking your info program what values it was compiled with. (Although you can probably find the actual value of DEFAULT_INFOPATH with this command:)

strings `which info` | grep /info: