Ok, if pg_ctl is launched, with ako 1.6, but how do I select an internal or external pg server via AkonadiTray ?

It was the issue, actually...

A few steps are needed actually:

run akonadictl stop,
in ~/.config/akonadi/akonadiserverrc, change StartServer=true to StartServer=false
you can also configure it directly in that file:
Change the "Host" line to point to the external server address,
Add a "User=" and "Password=" lines below and fill the holes with the correct values

and make sure you configured your Postgres server before trying to start Akonadi,
in your server postgres.conf, standard_conforming_strings must be enabled