If anyone wants to give it a try, the pinout that is directly on the keyboard membrane is below. The mating connector is Kyocera 046809626210846+. Pin 1 is the one on the right with the contacts facing up.
The backlight mating connector is ACES 51601-0040M-001, though it should be possible to find other brands that would fit. Backlight pinout is pins 1 and 2 negative and pins 3 and 4 positive. Pin 1 is the one on the left with the contacts facing up.