Hi @lukasl ,
You may be correct that there is a backup battery. (It looks as if there is a coin cell type battery but I cannot be sure of this, it might be a capacitor).
Here is an image of the Go Pro Hero 4 Black motherboard (taken from the ifixit parts shop). I've highlighted where I think that the "battery" is.
(click on image to enlarge for better viewing).
Here is a link to the ifixit GoPro Hero4 Black Expansion Port/Motherboard Replacement guide which should help you to gain access to the battery.
The battery can also be seen in the very first image in the guide (click on the magnifying symbol in the image) It is under the expansion port board so it is not visible in the other images in the guide.
Hopefully this is of some help
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