Would need some extensive automake magic.

Hmm, well with cmake you can do it as follows:

elseif(GIT_FOUND)
    execute_process(
        COMMAND ${GIT_EXECUTABLE} rev-list --max-count=1 HEAD
        WORKING_DIRECTORY ${CMAKE_SOURCE_DIR}
        OUTPUT_VARIABLE TR_VCS_REVISION
        OUTPUT_STRIP_TRAILING_WHITESPACE)
endif()

Code snippet directly taken from https://github.com/transmission/transmission/blob/main/CMakeLists.txt#L154-L160

Logically with makefile you can run something like $(shell git rev-list --max-count=1 HEAD) and will give you the same output as above.

Update: I have found this solution in case you would like to see how it can be implemented: https://stackoverflow.com/a/15376953