The first paragraph in
https://www.gnu.org/software/automake/manual/html_node/Linking.html
can be interpreted in a misleading way:

  "If you need to link against libraries that are not found by configure,
   you can use LDADD to do so. This variable is used to specify additional
   objects or libraries to link with; it is inappropriate for specifying
   specific linker flags; you should use AM_LDFLAGS for this purpose."

Last week, I interpreted this as "objects or libraries" being *.o, *.a,
and *.la files. And "linker flags" as including -L and -l options.
And I concluded that I should specify the -L and -l options in
*_LDFLAGS, not in *_LDADD, variables.

But that would not work because of these Automake generated rules
and variables:

LINK = $(CCLD) $(AM_CFLAGS) $(CFLAGS) $(AM_LDFLAGS) $(LDFLAGS) -o $@
test_bind_LINK = $(CCLD) $(AM_CFLAGS) $(CFLAGS) $(test_bind_LDFLAGS) $(LDFLAGS) -o $@

test-bind$(EXEEXT): $(test_bind_OBJECTS) $(test_bind_DEPENDENCIES) $(EXTRA_test_bind_DEPENDENCIES)
        @rm -f test-bind$(EXEEXT)
        $(AM_V_CCLD)$(LINK) $(test_bind_OBJECTS) $(test_bind_LDADD) $(LIBS)


Here's a proposed slight rewording that avoids this ambiguity.