Since one of my bicycles got the same Gazelle 02978 backlight:
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Outside of Gazelle 02978 backlight
Inside of Gazelle 02978 backlight
The button on the back side (which you can press through the outer housing under the luggage carrier), is a simple on-off toggle, but you have to wait about 2 seconds between pressing twice (otherwise it won’t recognise the second press).
If I ever need to replace it, this is the current (at time of writing early 2022) replacement part number 8717118039984.
The Wiert Corner - irregular stream of stuff 