1. Do the headlights come on for a few seconds and then go off in sync with the clicking sound?
2. Did you click the dimmer and retry switch?
3. How long ago was truck converted to 12V. Long before this happened?
4. Any wiring done recently? Any lights added or other accessories/components added, removed, replaced recently? (I know you said none, just rechecking). Any mechanical work that required electrical to be played with?
5. ALL bulbs including headlights changed to 12V?
6. Have you checked whatever fuses you have?
7. How many "PARKING" lights come on and stay on with first position, front and rear?
8. Any relays added? Relays click.
9. Headlights 12V sealed beam, non halogen or other than orig type?
Check your battery terminals/cables, especially ground at battery post and other end. Clean and renew to shinny.
Put your hand under dash and feel the switch as it "CLICKS" to be sure the noise is the switch itself. If it is the thermal breaker on the switch, it takes 42 Amps to trip it.
Take a good look at the inner fender headlight terminal blocks.
If all 9 questions are answered and you find nothing amiss visually, we may follow up a bit........ and then can proceed with electrical troubleshooting.