I try to add a custom action to the menu shown in the picture.
But I don't know the Location ID for that... or is it not possible to add there a custom context?
As you could maybe see from links exposed by Robert, these are quite fixed (even more than MSDN Ids http://wiki.customware.net/repository/pages/viewpage.action?pageId=69173255) as defined in the platform.
To my knowledge, you cannot add your own, but you could add your own items or hide items via Custom Actions. You could use the Control Delegate (http://msdn.microsoft.com/en-us/library/ms463169(v=office.14).aspx) alternatives to inject your own controls if none fit your bill (http://msdn.microsoft.com/en-us/library/ms470880(v=office.14).aspx or http://zimmergren.net/technical/sp-2013-some-new-delegatecontrol-additions-to-the-sharepoint-2013-master-pages), as this is also a prefered alternative to total control and freedom for later extensibility in your master page.
Here is the MSDN documentation containing all Location ID:s.
This menu is called the Site Actions Menu