Headlights will click and go off. I would be able to put them back on but the problem keeps happening about every hour or so. My mechanic replaced the lighting module

This will need to be diagnosed by a hands on mechanic rather than over the internet, I would suggest the dealership as they will have better access to information from the manufacturer than other mechanics.

Run a new ground wire to the lights and ground it direct to your engine. My car was doing this even the heater and lights and radio cut out once in a while . My mechanic spent several hours trying to find the answer and finally he said I am going to try something and he ran a new ground from the engine and wallah It worked. For some reason the existing ground was not working and it was grounded to the body. its self. He said maybe rust on the body would not let the power flow right.

you have a ghost in the machine.

Your lights are getting to hot they shut down the relay until it cools go back to the original headlights your alt batt will thank you ,

Check your battery to make sure it has 12 volts. If the battery is weak, it won't crank.

"...headlights are hooked directly to the battery" suggests that a previous owner had issues and wired it that way.
The solution is put the circuit (not necessarily the original wiring) back to the factory state.

What's probably happened is a bad ground for the headlight assemblies somewhere. It may also be that a short developed in the wiring harness, a not uncommon problem with many makes.

What you (or your mechanic) need is the schematic to
a) disconnect the previous owner's work; then
b) trace the headlight/signal control circuits though the relays to the headlights and signals; then
c) rebuild / repair as needed.

This can be a lengthy process, be prepared to pay forthe work.

Headlights are one of the most important safety features on your car, but they can only do their job if they're properly maintained. It's not just burned out headlights that cause problems; headlights that are dim or incorrectly aligned can also lead to accidents. Fortunately, learning how to repair headlights is something even the least mechanically inclined person can do. When you know how to repair headlights yourself, you can save up to several hundred dollars on mechanic's fees. Here are some tips on how to repair headlights with common problems.

Headlights that don't turn on
If you're headlights aren't working at all, the most likely cause is a burned out bulb. All you need to do to repair the headlights is replace the bulb. If you have plastic lenses, you can take out the old bulb by removing the lens and unscrewing the bulb from the back of the lens. With glass headlights, though, you'll need to replace the whole glass. Since you're buying new bulbs anyway, consider picking up one of the new, brighter types of bulbs, such as the halogen or xenon types.
When you've got your replacement bulb, install it and turn on the lights. If the headlights still don't work, it's a sign of an electrical problem. Because electrical problems are relatively complicated to repair, take your car to a mechanic before you try to do anything else with the headlights. This will help. Thanks please keep updated. please please do rate the solution positively .thank you for using fixya

HAVE YOUR MECHANIC CHECK THE FUSEABLE LINK BY THE SOLENOID. IF THIS LINK IS BURNED THE ALTERNATOR CAN NOT SEND CURRENT BACK TO THE BATTERY. IF ONLY PARTIALLY BURNED IT MAY SEND CURRENT, BUT NOT FULL CURRENT TO KEEP UP WITH THE DEMANDS THE HEADLIGHTS PLACE ON THE BATTERY.

check the charge rate should be 13-14 volts, if lower check for alternator drive belt condition/tightness if ok replace alternator

Yes,you need to replace the inition switch. You will have to have a steering wheel puller, snap-ring pliers, and a few screw drivers an a socket set. It is a goood little job, but can be done in a few hours. But it could be the other inition switch which mounts on the side of the steering colum shaft. It is a switch the has to be adjusted so that the key moves all the part in the right position. It has two screws or two bolts to remove to install it and adjust it. It not to bad to do.