Clock turns off when the headlights are turned on

It's best to start with the simplest things first. Have you checked your dimmer switch? The dash lights, including the clock, will automatically get dimmer when the headlights are turned on but can be brightened by adjusting the dimmer switch. If that checks out, you can check the fuse panel next to make sure you don't have any blown fuses which could be affecting the clock. I've posted a diagram of the fuse panel below. Please let us know what you find out and if you need more help please don't hesitate to ask!