Since the the touch switch doesn't work, we discard that circuit board. Cut the 4 wires at the circuit board.

I soldered my wires together and covered with shrink tubing. I suppose you could use good insulated wire connectors instead.

Connect the 2 black wires together, the one from the USB board to the one going to the lamps.

Connect the red wire from the USB board to one of the switch wires. I used the red switch wire.

Connect the other wire from the switch to the white wire going to the lamps.

Screw the USB board back in place.