The backlight is pretty easy to identify. Look for the A and K pins on the FPCB (ribbon cable). They are almost certainly (A)node and (K)athode of the LED(s), furthermore the black tape (labelled CN3 on the FPCB) probably covers an SMD LED (or two) or a couple of zero ohm links. One other possibility is that the black tape might cover some configuration jumper pads used to set the interface mode.
Put your multimeter in diode test mode, and probe between the A and K pins, and you may well be rewarded with a dim glow from the backlight.
From there it is a matter of figuring out where those pins go on the main pcb.
Look closely at the image you posted of the FPCB, the interface might actually be relatively easy to figure out.
Although the controller has a bewildering array of possible interface modes, we can eliminate most of them due to the relatively low number of pins on the connector.
The connector itself has 18 pins, and one of those has been left blank, so that leaves 17, if we assume a minimum of two further pins, one each for power and gnd, and it appears two pins for the LED (although it may have a common ground or power pin, so it may only use one), then we only have 13 pins left, so we cant be using 16 bit parallel modes. It may be possible to further eliminate pins, since we may have a ground pin interleaved between each signal pin. If this is the case, then we may only be looking at six or seven signal lines.
If the gadget was still working, we could stick a logic analyser on it and get the right answer pretty quickly, but since it is not, we may need to eliminate the remaining modes by trial and error.
I presume the display doesn’t have a touch screen.
The button interface should also be relatively easy to figure out with the continuity tester on your multimeter too.