How to force mysqldump to produce /*!40101 SET character_set_client = utf8mb4 */;
I have checked out mysql-5.4.46, and searched client/mysqldump.c for "SET character_set_client".

It finds

[:~/Source/mysql-server/client]↥ 9c3a49ec84b* ± grep 'SET character_set_client' mysqldump.c
          "/*!50003 SET character_set_client  = %s */ %s\n"
          "/*!50003 SET character_set_client  = @saved_cs_client */ %s\n"
                  "SET character_set_client = utf8;\n"
                  "SET character_set_client = @saved_cs_client;\n");
                "/*!40101 SET character_set_client = utf8 */;\n"
                "/*!40101 SET character_set_client = @saved_cs_client */;\n",
            "/*!50001 SET character_set_client      = %s */;\n"
            "/*!50001 SET character_set_client      = @saved_cs_client */;\n"


From this, it seems that some instances of "SET character_set_client" are fixed at utf8 in this version and are not even variable.

One of them is the /*!40101 SET character_set_client = utf8 */; line you quote as being faulty.

After checking out current 8.0 HEAD, I get

[:~/Source/mysql-server/client]↥ 8.0* ± grep 'SET character_set_client' mysqldump.cc
          "/*!50003 SET character_set_client  = %s */ %s\n"
          "/*!50003 SET character_set_client  = @saved_cs_client */ %s\n"
                  "/*!50503 SET character_set_client = utf8mb4 */;\n"
                  "SET character_set_client = @saved_cs_client;\n");
              "/*!50503 SET character_set_client = utf8mb4 */;\n"
              "/*!40101 SET character_set_client = @saved_cs_client */;\n",
        "/*!50001 SET character_set_client      = %s */;\n"
        "/*!50001 SET character_set_client      = @saved_cs_client */;\n"


So while there are still fixed SET character_set_client statements, they now default to utf8mb4. Note that all other statements are %s-ed, and further checking shows they defer to whatever you --default-character-set=utf8mb4 in your commandline.

My suggestion is you dump, possibly remotely, with a newer mysql 8.0 binary. In general, upgrading is adviseable, as 5.6 is an outdated unsupported version of the database (yes, I know, it's complicated. It always is.)