the mysql.ping item from the template MySQL App does not do the job when MySQL is down.

The reason invoked is: Can't connect to MySQL server on '127.0.0.1' (111)'Check that mysqld is running on 127.0.0.1 and that the port is 3306.You can check this by doing 'telnet 127.0.0.1 3306

I try to monitor my MySQL instance through a TCP connection, not by socket, because it's running in a docker container.

How to solve this :
In the /etc/zabbix/zabbix_agentd.d/userparameter_mysql.conf, provided by the RPM package, the check command should the "-s" argument.

Original input:
UserParameter=mysql.ping,HOME=/var/lib/zabbix mysqladmin ping | grep -c alive
Fixed input
UserParameter=mysql.ping,HOME=/var/lib/zabbix mysqladmin -s ping | grep -c alive