From the link you provided:

C TAP Harness can run Perl test scripts directly and interpret the results correctly, and similarly the Perl Test::Harness module and prove command can run TAP tests written in other languages using, for example, the TAP library that comes with C TAP Harness. You can, if you wish, use the library that comes with C TAP Harness but use prove instead of runtests for running the test suite.

L-LL-L--L-LL-L--L-LL-L--
-R--R-RR-R--R-RR-R--R-RR
B--B--B--B--B--B--B--B--
H---H---H---H---H---H---
(the triplet paradiddle with high-hat)

it seems that to make a correct use of that library and the power of prove I am going to need more than the cursory knowledge I have of the autotools.
I shall start reading some books I had put away for such a time right away

Great and many thanks for your wise counsel and hints fellow monk you have set me on a path of better learning and understanding.

Update: after fiddling around I found out that any makefile in the tests subdirectory is ignored, so I probably am missing something when writing my main Makefile.am. After a bit of fiddling around I still have the error output, yet when I run make check-local I get undefined references error
This is not surprising since the gcc command run does not include either the tap files or the main program's c files

YAU(yet another update) I managed to make it work but I did not follow the c tap harness author instructions : I added a line to my Makefile.am so it builds the test executable before running the test suite, that way everything works fine. Still it feels a bit unelegant and like cheating, am I doing things right?

So after some studying I think I'm starting to get autotools to do what I want (at least autoconf et automake) right now I'm confronted with a bit of a conundrum :

For any test programs that need to be compiled, add build rules for them in Makefile.am, simliar to:
tests_libtap_c_basic_LDADD = tests/tap/libtap.a

this line is quite a mysterious : as I understand it, if I have in my tests directory a subfolder containing tests for a specific c file (lets call that test file specific_tests.c) to have the harness run those tests I'd need to add to Makefile.am the following line :

specific_tests_LDADD=tests/tab/libtap.

Thing is if I add this line and then autoreconf I got the following output :

Makefile.am:10: warning: variable 'specific_tests_LDADD' is defined bu
+t no program or
Makefile.am:10: library has 'specific_tests' as canonical name (possib
+le typo)
[download]

I must add that if I compile specific_tests myself into a specific_tests.t output file make checklocal runs perfectly "