Try rewiring the plug, there seams to be a lot of heat damage on the neutral (the blue wire), also there are strands sticking out for the live wire (the brown wire). a loose terminal could maybe be to blame. That is what I would try first.
Yes that looks perfect.
Before drilling the hole in the cover, triple check the clearance space behind the intended hole location and that the cable run from the light is clear and not too far away from the terminals.
I'm guessing that the two coin/credit cables go to the same place on the circuit board, which are probably two "push to make switches".
Can you open it up and have a look to see if there is a problem with the connection ?
Personaly, I would keep them and plug in surround sound system.
To have these wires already hidden and installed is a God send !
I've never had one untill three years ago and I'll always have one now.