Your capacitor stays on when car is turned off?

The cap is not actually on but it is rather the display.

The display will only stay light up until the voltage levels out to what the battery is at. Sometimes it can take awhile for it to go off. Sometimes you would think it is always on because when you open your trunk the display is light up. What actually happens is that when you open the trunk there is a slight demand from the battery which causes the display to light up.

This is normal and you should not worry about it. It is not going to drain your battery at all and it is not doing any harm.