You can either trigger the export of all defined exports like this:
Object dbConnector=Model.find("Tools/DatabaseConnectors/DatabaseConnector1");
function_s(dbConnector,"exportAll");
Or trigger a single export:
Object dbConnector=Model.find("Tools/DatabaseConnectors/DatabaseConnector1");
treenode dbexport=variables(dbConnector).subnodes["exporters"].first; // the first in the list of exports.
function_s(dbConnector,"exportSingle",dbexport);
Since it uses function_s calls, you may need to revise this code in the future, so if you need to invoke it in many places I'd place it in a user command and call that from multiple places instead.