Check the connections, use a multimeter. At the gear selector check the resistance when pressing on the paddles, measure between a ground point and each of the wires coming from the paddles to the gear selector harness. When pressing on the paddle and measuring on the correct wire there should be little (wire resistance) to no resistance, and when no paddle is pressed there should be infinite resistance.
There is one thing that I reacted on in this guide and the LCI paddles is that the 3-pin connector socket from each paddle is not connected like this guide suggests. Look at "installation part 1 - paddles to mfb", there are 2 wires coming from my LCI paddles that are connected to pin 1 and 3 but this DIY suggests that they should be connected to pin 2 and 3. I would think that this could be your problem depending on the production date of your multifunction buttons, but you could try moving one wire from the each paddle to pin 2 on the connector socket and test the paddles again.