Somewhat guessing here - Are you possibly trying to use an (unconfigured)
external mysql instance?
Right-click the akonadi tray icon=>configure=>server config? If it's
external (and that's what you want) - check you ran mysql_install_db (I
think the mysql ebuild eeinfo's the config steps).

FWIW I have the same error about timezones in
$HOME/.local/share/akonadi/db_data/mysql.err (using 'internal' mysql
instance).

Cheers,
malc.