How can I troubleshoot faulty motion-sensor security lights on a timer?

This is a very common type timer for light, sprinkler pumps, pool filters, etc. Start out by pulling out the yellow disk and turn it to the current time. Monitor it to see if it keeps proper time. There is an "off" tab still on the disk but no "on" tab. It looks like it might have fallen off and is still in the box. This would prevent the lights from going on. There is also a silver lever that says "on" and "off". This lever is a manual switch for anything hooked up to it and it will over ride the timer so start checking that to see if the lights go on. Then turn off the power and swing that plastic cover out of the way and check the wiring for power. Also check the bulbs to make sure they are good.

Just so you know Motion sensor lights do have a finite amount of life before they expire. Depending on the brand a motion sensor can be expected to last anywhere's from a few months to several years. The latest LED models have longer bulb life, but it's usually the motion sensor that expires first.

Pull one of them from the round box and check for power with a voltage tester. This is the surest way to know if the light is supposed to be working.

Also, unless you know otherwise, most motion sensors are commonly controlled by a toggle switch located on the interior of the house by a door leading outside.