12mm socket wrench for overhauling pedals

According to this:
https://www8.garmin.com/manuals/webhelp/vector3/EN-US/GUID-1614637F-1B8A-466C-A208-9CA9EA626921.html
On step 5 you need a 12mm socket wrench to unscrew the spindle nut. I have tried 5 different ones and none of them is small enough to fit in the pedal body and reach the nut.
Can anyone who has managed to do it post a link to the socket wrench they used? Alternatively, can someone from Garmin recommend a product that would work?

Thanks