As we can see in the screenshots below, the D6503 Sirius does show the Stamina Mode on icon (that "+" sign next to the battery icon) while the phone is charging. With the Stamina Mode off, the icon is gone.
The Stamina Mode is supposed to increase the standby time of your battery by up to four times. The feature is able to achieve this by reducing the background activities of your apps. One minute after the screen turns off, data traffic is blocked and background activities are prevented from turning on the screen. Of course, as soon as you open the screen, everything starts working once again.
Screenshots from Sony D6503 Sirius show Stamina Mode on icon
1. Stamina Mode is on
2. Stamina Mode is off
Thanks, Anonymous Tipster!