diff --git a/src/keymap.c b/src/keymap.c
index 295b209f06b..a01dee1476b 100644
--- a/src/keymap.c
+++ b/src/keymap.c
@@ -1721,33 +1721,12 @@ means to return the active maps for that window's buffer.  */)
 	  /* For a mouse click, get the local text-property keymap
 	     of the place clicked on, rather than point.  */
 
-	  if (POSN_INBUFFER_P (position))
-	    {
-	      Lisp_Object pos = POSN_BUFFER_POSN (position);
-	      if (FIXNUMP (pos)
-		  && XFIXNUM (pos) >= BEG && XFIXNUM (pos) <= Z)
-		{
-		  local_map = get_local_map (XFIXNUM (pos),
-					     current_buffer, Qlocal_map);
-
-		  keymap = get_local_map (XFIXNUM (pos),
-					  current_buffer, Qkeymap);
-		}
-	    }
-
-	  Lisp_Object pos_area = POSN_POSN (position);
-	  if (EQ (pos_area, Qmode_line) || EQ (pos_area, Qheader_line))
-	    {
-	      /* For clicks on mode line or header line, ignore the maps
-		 we found at POSITION, because properties at point are
-		 not relevant in that case.  */
-	      local_map = Qnil;
-	      keymap = Qnil;
-	    }
+	  local_map = Qnil;
+	  keymap = Qnil;
 
 	  /* If on a mode line string with a local keymap, or for a
 	     click on a string, i.e. overlay string or a string
-	     displayed via the `display' property, consider only the
+	     displayed via the `display' property, first consider the
 	     `local-map' and `keymap' properties of that string.  */
 
 	  if (CONSP (string) && STRINGP (XCAR (string)))
@@ -1763,6 +1742,26 @@ means to return the active maps for that window's buffer.  */)
 		}
 	    }
 
+	  Lisp_Object buffer_posn = POSN_BUFFER_POSN (position);
+	  /* Then, if the click was in the buffer, get the local
+	     text-property keymap of the place clicked on.  */
+
+	  if (FIXNUMP (buffer_posn)
+	      && XFIXNUM (buffer_posn) >= BEG && XFIXNUM (buffer_posn) <= Z)
+	    {
+	      /* The properties in POSN_STRING take precedence, if set. */
+	      if (NILP (local_map))
+		local_map = get_local_map (XFIXNUM (buffer_posn),
+					   current_buffer, Qlocal_map);
+
+	      if (NILP (keymap))
+		keymap = get_local_map (XFIXNUM (buffer_posn),
+					current_buffer, Qkeymap);
+	    }
+
+	  /* Finally, fall back on the buffer's local map. */
+	  if (NILP (local_map))
+	    local_map = BVAR (current_buffer, keymap);
 	}
 
       if (!NILP (local_map))
diff --git a/test/src/keymap-tests.el b/test/src/keymap-tests.el
index 950c741a6dd..0d203f6fcb0 100644
--- a/test/src/keymap-tests.el
+++ b/test/src/keymap-tests.el
@@ -509,25 +509,36 @@ g .. h		foo
     ;; From the parent this time/
     (should (equal (keymap-lookup map "u") #'undo))))
 
+(defun keymap-test--get-maps (posn)
+  (let ((maps (current-active-maps nil posn)))
+    ;; The local map should always be present.
+    (should (memq (current-local-map) maps))
+    maps))
+
 (defun keymap-test--maps-for-posn (area string)
-  (current-active-maps
-   nil
+  (keymap-test--get-maps
    ;; FIXME: This test would be better if this was a real position
    ;; created by a real click.
-   `(,(selected-window) ,area (1 . 1) 0 (,string . 0) nil (1 . 1) nil (1 . 1) (1 . 1))))
+   (let (;; If AREA is passed, the click isn't in the buffer; otherwise
+         ;; it's at position 1.
+         (pos (if area nil 1)))
+     `(,(selected-window) ,area (1 . 1) 0 (,string . 0)
+       ,pos (1 . 1) nil (1 . 1) (1 . 1)))))
 
 (ert-deftest keymap-test-keymaps-for-non-buffer-positions ()
   "`current-active-maps' with non-buffer positions.  (bug#76620)"
   (with-temp-buffer
     (pop-to-buffer (current-buffer))
     (let ((keymap (make-sparse-keymap "keymap-at-point")))
+      (use-local-map (make-sparse-keymap "buffer-local-map"))
       (insert (propertize "string" 'keymap keymap))
       (goto-char (point-min))
-      (should (memq keymap (current-active-maps)))
+      (should (memq keymap (keymap-test--get-maps nil)))
       (should-not (memq keymap (keymap-test--maps-for-posn 'mode-line nil)))
       (should-not (memq keymap (keymap-test--maps-for-posn 'mode-line "s")))
-      (should-not (memq keymap (keymap-test--maps-for-posn nil "s")))
+      (should (memq keymap (keymap-test--maps-for-posn nil "s")))
       (should (memq keymap (keymap-test--maps-for-posn nil nil)))
+      (should (memq keymap (keymap-test--get-maps "a")))
       (let* ((mode-line-keymap (make-sparse-keymap "keymap-in-mode-line"))
              (s (propertize "string" 'keymap mode-line-keymap)))
         ;; Respect `keymap' in the string clicked on.