Just join crimp , solder and extend cables etc
You could bury them in wall and put a face plate on top after
I would open the plaster up more towards ceiling and fit panel higher up if possible then joins can be inside panel
Do you have a better picture?
Dude
Simple process for you
Swap both keypads round
If keypad one works in position 2 atleast you know for sure to an extent the cable power and coms is good
Then it has to be addressing and programming or the keypad itself