Each time you step on a switch, the path in this room grows longer.  You’re up against a time limit, so don’t hesitate to shoot any monsters that get in your way.

As before you need to light up the green path all the way to the locked door.  However, to reach the final switch (shown in the picture) you’re going to have to stray from the path.

The trick is to follow the green path all the way to its end before leaving it and making a run for the final switch.  Carry on around the loop and you should be able to get back onto the path before its colour fades.  You can then walk along it right up to the door.