They're connected to the battery all the time. Without the display turned on, they take very little energy. If you ever disconnect a car battery, you have to reset the clock.
Thats a good question.
By logic I would guess it consumes electricity from the battery without giving you notice, or the actually put in quartz batteries. Quartz resonnates on a timed basis and many clocks work on that, still needs batteries. Or it had inside a small generator that produces electricity when you move the object.
Thats because the batterie is still giving it electricity to the device... so for example... if you take the batterie from a car for more than a couple of min. it will completly shut off and the time will start from zero once you put it back... the same thing with your gamboy.. if you where to take the batterie out it would start from zero and you would have to config. the time. So as long as there is source of elec. feeding the device it will keep the time.
the battery is on all the time and it draws its power from it
And not just in cars, anything that has an internal clock. I remember my Gameboy Color kept track of time in Pokemon Gold.
