The video signal from the CPU has two different GPU logic paths going to the IG or via the DG, then the signal has three different paths by default the internal display via the internal DisplayPort (iDP) connection, then you have either the HDMI port or lastly the Thunderbolt ports treating the connection as a DisplayPort connection.

Depending on what you’ve set within the Energy Saver control panel if you’ve checked off the Automatic graphics switching. This sets the IG as the preferred graphics services unless the application tells it otherwise. Some actions within the startup settings will also force the IG as the preferred graphics services. Otherwise the DG will be used if available (the IG only models don’t offer this setting).

OK, now that we have a handle on how this all works we can try to figure out whats happening with your system.

Which are you using for your external display? The HDMI connection or the Thunderbolt connection?