Backlights can be tested by connecting them to a known good inverter. You can use one of the inverters they sell for case moding. Just provide a 12V input for it and connect your backlight to one of the output sockets. If your backlight illuminates then it is OK and the fault lies elsewhere. A pink or red hue to the screen is nearly always a sign of a failing backlight and if this happens it is well worth replacing the backlight as the only other thing that can cause this is a faulty screen.

Remember backlights work on an AC Voltage of around 1000v and although the wattage is very small can give you a nasty shock and could prove fatal if you have a pacemaker or similar.