Daughters 2002 Jeep Liberty, the headlights cut out intermittently for no reason.?

Yes, ALL of the exterior and interior lighting on this vehicle is controlled by the BCM (body control module) The headlights are controlled through the FCM (front control module) To do any diagnosis on this vehicle requires a compatible full function scan tool that has BCM communication ability! What is trying to be discovered is if the problem is on the input side of the BCM or the output side! One other thing that is not clear is do ALL the lights (parking/tail lamps) go out or JUST the headlights?

Jeep Liberty Headlights

The clicking sound you are hearing is probably the electrical relay for the headlights.

How the relay works: when you turn on the lights, an electrical magnetic coil is activated which attracts a metallic strip. The metallic strip is what completes the circuit to turn the lights on. You can test the relay with a couple of wires and the car battery. Either the relay is faulty or the connectors to the headlight assembly are faulty. Disconnect them and check if they are burned or black.

A lot of vehicles have a Fuse for the Headlights, which is overload sensitive, and will interrupt and reset it's self. OEM is a "habitat" for cheaper items, which can be replaced by a much better piece. That fuse is not real cheep, but, it's the first place to go for this problem.

That'd be the simple way out of this but...

In some instances, that "circuit breaker" is located in the Headlight Switch. So, if you don't find it in the fuse box, then, there's a little more expense and trouble ahead for this replacement.

Good luck.

My guess would be either a cheap/bad component or a heat issue due to a bad connection somewhere making a relay or switch act up.

Here's a very interesting article that looks like it should should prove way more helpful than me:

http://www.jeepfan.com/projects/brighten-your-ligh...