[...] doesn't make sense when the official Sky3DS team emails me saying it works with ANY 3DS and ANY microSD card. So I don't know!
Because it is wrong, all the existing microSD cards are not compatible with but with or without MicroSD card, the LED must blink when inserted.
The issue must be bad contact between Sky3DS card and cartdrige Slot-1 connectors.
See if the plastic card is deformed/curved.