diff --git a/C4/Biblio.pm b/C4/Biblio.pm
index 5ddd7c7272..ac35b38777 100644
--- a/C4/Biblio.pm
+++ b/C4/Biblio.pm
@@ -824,8 +824,11 @@ sub LinkBibHeadingsToAuthorities {
                         # thesaurus instead of relying on AddAuthority()'s LCSH-only default.
                         # AddAuthority() only defaults 008/040 when they aren't already present
                         # on the record, so pre-populating them here is sufficient - no change
-                        # to AddAuthority() itself is needed.
-                        if ( $heading->{thesaurus} ) {
+                        # to AddAuthority() itself is needed. Skip this when the heading's
+                        # thesaurus couldn't actually be identified (bug 31925 comment 30) - in
+                        # that case the site's own MARCAuthorityControlField008 default should
+                        # apply, the same as it always has, rather than being overridden.
+                        if ( Koha::Authority->has_known_thesaurus( $heading->{thesaurus} ) ) {
                             my $date = POSIX::strftime( '%y%m%d', localtime );
                             $marcrecordauth->insert_fields_ordered(
                                 MARC::Field->new(
diff --git a/Koha/Authority.pm b/Koha/Authority.pm
index d3f76ff106..b932ca250c 100644
--- a/Koha/Authority.pm
+++ b/Koha/Authority.pm
@@ -324,6 +324,41 @@ our $MARC21_THESAURUS_TO_CONTROL_FIELD_008_11 = {
     notspecified  => '|',
 };
 
+# The subset of $MARC21_THESAURUS_TO_CONTROL_FIELD_008_11 keys that
+# C4::Heading uses to mean "no specific thesaurus could be identified from
+# the source heading's indicators" (a blank/unrecognised indicator 2, or
+# indicator 2 = 4), rather than a genuine, named thesaurus. Kept private -
+# callers should go through has_known_thesaurus() rather than consulting
+# this directly.
+my $UNDEFINED_THESAURUS_VALUES = {
+    notdefined   => 1,
+    notspecified => 1,
+};
+
+=head3 has_known_thesaurus
+
+    if ( Koha::Authority->has_known_thesaurus($thesaurus) ) { ... }
+
+Returns true if C<$thesaurus> (as derived by C4::Heading from MARC
+indicator 2 / subfield $2, e.g. 'lcsh', 'mesh', or a raw $2 code such as
+'fast') identifies an actual thesaurus. Returns false if C<$thesaurus> is
+undefined, or is one of the placeholder values C4::Heading returns when
+no thesaurus could be identified from the source heading's indicators
+('notdefined', 'notspecified').
+
+Callers that want to code a new authority's 008/11 (and 040$f) from a
+heading's thesaurus should check this first, and leave the site's own
+default (I<MARCAuthorityControlField008>) in place otherwise.
+
+=cut
+
+sub has_known_thesaurus {
+    my ( $class, $thesaurus ) = @_;
+
+    return 0 unless defined $thesaurus;
+    return $UNDEFINED_THESAURUS_VALUES->{$thesaurus} ? 0 : 1;
+}
+
 =head3 default_marc21_008
 
     my $default_008 = Koha::Authority->default_marc21_008;
diff --git a/t/db_dependent/Biblio.t b/t/db_dependent/Biblio.t
index 975517886a..5fda819a4e 100755
--- a/t/db_dependent/Biblio.t
+++ b/t/db_dependent/Biblio.t
@@ -17,7 +17,7 @@
 
 use Modern::Perl;
 
-use Test::More tests => 27;
+use Test::More tests => 28;
 use Test::NoWarnings;
 use Test::MockModule;
 use Test::Warn;
@@ -1115,7 +1115,7 @@ subtest "LinkBibHeadingsToAuthorities record generation tests" => sub {
 };
 
 subtest "LinkBibHeadingsToAuthorities codes new authorities with the source thesaurus (bug 31925)" => sub {
-    plan tests => 7;
+    plan tests => 11;
 
     my $biblio_mod = Test::MockModule->new('C4::Linker::Default');
     $biblio_mod->mock(
@@ -1171,6 +1171,35 @@ subtest "LinkBibHeadingsToAuthorities codes new authorities with the source thes
         substr( $authority->field('008')->data(), 11, 1 ), 'a',
         'Non-subject heading (700) keeps the default LCSH 008/11=a coding, unaffected by this fix'
     );
+
+    # Case 5: blank ind2 (thesaurus not identified at all) - must respect the
+    # MARCAuthorityControlField008 syspref default, not be forced to 'z' (bug 31925 comment 30)
+    $biblio = $builder->build_sample_biblio();
+    $record = $biblio->metadata->record;
+    $field  = MARC::Field->new( '650', '', ' ', 'a' => 'Unidentified thesaurus' );
+    $record->append_fields($field);
+    LinkBibHeadingsToAuthorities( $linker, $record, "", undef, 650 );
+    $authority = GetAuthority( $record->subfield( '650', '9' ) );
+    is(
+        substr( $authority->field('008')->data(), 11, 1 ), 'a',
+        'Blank ind2 (no thesaurus identified) keeps the syspref default 008/11=a, not forced to z'
+    );
+    is( $authority->subfield( '040', 'f' ), undef, 'Blank ind2 (no thesaurus identified) gets no 040$f' );
+
+    # Case 6: ind2=4 (explicitly "source not specified") - must also respect a customised
+    # MARCAuthorityControlField008 syspref default rather than being forced to '|'
+    t::lib::Mocks::mock_preference( 'MARCAuthorityControlField008', '|| acn||aabn           | a|a     d' );
+    $biblio = $builder->build_sample_biblio();
+    $record = $biblio->metadata->record;
+    $field  = MARC::Field->new( '650', '', '4', 'a' => 'Source not specified' );
+    $record->append_fields($field);
+    LinkBibHeadingsToAuthorities( $linker, $record, "", undef, 650 );
+    $authority = GetAuthority( $record->subfield( '650', '9' ) );
+    is(
+        substr( $authority->field('008')->data(), 11, 1 ), 'n',
+        'ind2=4 (source not specified) respects a customised syspref default 008/11=n, not forced to |'
+    );
+    is( $authority->subfield( '040', 'f' ), undef, 'ind2=4 (source not specified) gets no 040$f' );
 };
 
 subtest 'autoControlNumber tests' => sub {