I think that it would be a good idea to mention PROVE_TESTS as well. I personally use and abuse of it, and documenting it instead of keeping it hidden in Makefile.global.in is good for new developers and testers.
Proposal of patch attached.
Good plan. I thought it was already mentioned, but that mention is only in src/test/perl/README where I doubt people routinely running the tests will see it. I think I put it there mainly to help people writing/fixing tests.