To keep the backlight on, you may think it makes sense to call SystemIdleTimerReset() repeatedly. (Or at least I thought so.) But this doesn't work on all (most?) phones:

[DllImport("coredll.dll")]
public static extern void SystemIdleTimerReset();

public static void Main(string[] args) {
    // Reset the idle timer every 10 seconds, starting now
    var Timer = new Timer(SystemIdleTimerReset, null, 0, 10000);

    // do useful stuff...
}

This does work, however:

[DllImport("coredll.dll")]
public static extern void SystemIdleTimerReset();

[DllImport("coredll.dll")]
public static extern IntPtr SetPowerRequirement(
    string device, int deviceState, int deviceFlags, IntPtr systemState, int stateFlags);

[DllImport("coredll.dll")]
public static extern int ReleasePowerRequirement(IntPtr handle);

public enum CEDEVICE_POWER_STATE {
    PwrDeviceUnspecified = -1,
    D0 = 0, // full on
    D1,
    D2,
    D3,
    D4, // off
    PwrDeviceMaximum
}

public static void Main(string[] args) {
    var Timer = new Timer(SystemIdleTimerReset, null, 0, 10000);
    IntPtr handle = SetPowerRequirement(
        "BKL1:", 
        (int) CEDEVICE_POWER_STATE.D1, 
        1, 
        IntPtr.Zero, 
        0
    );
    
    // do useful stuff...
    
    ReleasePowerRequirement(handle);
}

SetPowerRequirement() forces the system to remain in a higher power consumption state than it otherwise would be in. CEDEVICE_POWER_STATE.D0 is "Full On"; D1 is "Low On" and D4 is "Off." Be sure to ReleasePowerRequirement() when you're done.

The BLK1: is the backlight device name. It's been the same on all the phones I've tested on, but there aren't any guarantees. To find out what the name is on your particular phone, look in the registry in HKLM\Drivers\BuiltIn. There will be a key called Backlight or Frontlight or something similar. The device name seems to be determined by the values Prefix and Index (on my phones these are BKL and 1).