I've just been looking into this. I did a search to see if there's any more knowledge on the subject before I start soldering, but found this question instead
It seems odd that it was just asked a few days ago.
The Output command would cover turning C2 on and off, to control the backlight:
Output Command (255)
Outputs C.2, C.1 and C.0 are all controlled by the lower 3 bits of an output
which is prefixed by the number 255.
serout B.7,N2400,(255,%00000111); all outputs on
pause 1000
serout B.7,N2400,(255,%00000000); all outputs off
C2 off would turn the backlight on; C2 on would turn it off. If you don't need the other two outputs for anything, just turn them all on and off together, I guess. For using them independently, you'd have to rewrite the "firmware" for the module, i.e. the .BAS program that controls it.
I can't easily draw a diagram, but if you check the connections to those pads in the corner near the stereo socket, you'll see how to do it. There are pads for a base or gate resistor from C2 (near that end of the LCD connector), to a PNP transistor, or P-channel FET, on the corner three pads. The one on the corner is Vdd (5V), for the emitter of the transistor or source of the FET. The collector or drain goes in the third hole and that's connected across to the left one of the next pair of pads. The right hand one of those pads is square and is connected to pin 15 of the LCD module connector (A for anode) - that's not connected, in the photo, and neither is 16 (K for cathode, which is just connected to ground). The order of the pins is 15, 16, 1, 2... 14, taken from the left hand corner of the board in that photo.
I think the best thing to do is use a diode to connect that square pad to the collector or drain, because the LCD backlight probably wants 4.2V, not 5V (Winstar ones do).
I'm sure that's confusing to read, and a diagram would be better, but trace out the connections with a multimeter and it should make more sense, now you know what you're aiming for
To summarise:
C2 feeds into the base of a PNP transistor or the gate of a P channel FET via a resistor. There are pads for the resistor, and a transistor or FET with the base or gate in the middle. The transistor/FET may need to source upto 250mA, so a FET might be better than a transistor. You probably need a diode between the collector (or drain) and the A for anode pin of the LCD, to get the correct backlight voltage. There are pads for that too.
I bought a backlit 16x2 module on ebay (Chinese seller) to uprade my AXE133. The connections for the backlight are at the other end - 15 follows 14, and the placing of the set of pads on the board is different, so it doesn't line up as well, but it's basically the same module with a backlight added. I've tested the backlight with a single cell lipo (4.2V max). It's nice and blue