Header absolute paths for GCC

I am looking to print a list of absolute paths to a specific header file used by gccwithout compiling anything (or specifying a particular compile target, like with gcc -M). E.g., the following would print a list of absolute paths with all matches for limits.h found in the appropriate directories:

gcc <flag/command> limits.h

A (non-)solution that returns only working header files is to simply create a check.c, #include all desired header names there, and run gcc -M check.c.

Another solution, (albeit using bash stuff) is found in this answer and here.

Related questions that didn't quite have what I want:

• How can I see the location of a header included with #include?
• Where does gcc look for C and C++ header files?
• How to I find the filename of a library via the library name?
• How can I find the full file path given a library name like libfoo.so.1?
• gcc -print-file-name=libc.a prints absolute path in the strange form