neepie:
in which case you bypass the transistor
Bypass the backpacks transistor? I could just replace that jumper with a resistor?
You figure out whether the transistor is connected between ground (pin 1) and the cathode of the backlight (pin 16) or between Vcc (pin 2) and the anode of the backlight (pin 15) and connect a resistor between that two pins to set the minimum (night-time) brightness, and use the software control to switch to maximum brightness.
I haven't looked closely at the jumpers in the backpacks I have here (quite a few!), but presumed they disabled the backlight entirely if removed. If they in fact put the backlight on irrespective of software control (which does make more sense as it allows for software not doing so), then yes, you would simply put the resistor in place of the jumper.